Treatment validation systems and methods

ABSTRACT

Treatment validation techniques include generating a modified treatment target from an original treatment target using a modification process, and comparing induced aberrations provided by the original and modified treatment targets, so as to verify the modified treatment target or the modification process. In some cases, a modification process may include a deconvolution process, a low pass filter process, a scaling process, or an adjustment process. The induced aberrations may include high order aberrations, such as spherical aberration.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a non-provisional of and claims the benefit ofpriority to U.S. Provisional Patent Application No. 61/901,216 filedNov. 7, 2013. This application is related to U.S. Patent Application No.61/708,815 filed Oct. 2, 2012, U.S. Patent Application No. 61/871,120filed Aug. 28, 2013, U.S. patent application Ser. No. 14/044,650 filedOct. 2, 2013, and U.S. patent application Ser. No. 14/453,068 filed Aug.6, 2014. This application is also related to U.S. Pat. No. 7,926,490issued Apr. 19, 2011, U.S. patent application Ser. No. 13/051,452 filedMar. 18, 2011, and U.S. patent application Ser. No. 13/554,276 filedJul. 20, 2012. Further, this application is related to U.S. Pat. No.8,409,178 issued Apr. 2, 2013 and U.S. patent application Ser. No.13/854,760 filed Apr. 1, 2013 (now U.S. Pat. No. 8,663,207 issued Mar.4, 2014). The entire content of each of the above filings isincorporated herein by reference for all purposes.

BACKGROUND OF THE INVENTION

Embodiments of the present invention relate generally to the field ofoptical correction, and in particular encompass methods, devices, andsystems for evaluating treatments intended for administration topatients presenting vision conditions.

In a typical refractive surgical procedure, aberrations of the patient'seye are examined with wavefront analysis or other measurementprocedures. In turn, the measurement information can be used to generatea treatment for the patient. Laser eye surgery systems and other visiontreatment techniques often involve the use of such treatments.

Although current and proposed treatment devices and methods may providereal benefits to patients in need thereof, still further advances wouldbe desirable. For example, there continues to be a need for improvedablation systems and methods that accurately assess, verify, andvalidate treatments. Embodiments of the present invention providesolutions that address certain limitations which may be associated withknown techniques, and hence provide answers to at least some of theseoutstanding needs.

BRIEF SUMMARY OF THE INVENTION

Embodiments of the present invention encompass systems and methods forvalidating or qualifying treatments for use in refractive surgeryprocedures. These techniques ensure that treatments are generated asintended for a particular patient.

Hence, embodiments of the present invention provide improvements inablation control, laser, ablation profile generation, treatmentgeneration, and process or software verification and validation.Relatedly, techniques for evaluating a treatment as described herein canbe used to increase the safety of an ophthalmologic refractive surgery.

In some cases, embodiments of the present invention encompass systemsand methods for treatment validation based on the preservation of loworder aberrations. In some cases, embodiments of the present inventionencompass systems and methods for treatment validation based onsphere-cylinder coupling. In some cases, embodiments of the presentinvention encompass systems and methods for treatment validation basedon high order aberrations, such as the addition of spherical aberrationwith the use of deconvolution.

The post-operative induction of high-order aberrations (HOAs),especially spherical aberration (SA), remains an important issue forlaser vision correction technology.

It has been found that post-operative cornea remodeling is a significantroot cause of SA induction. One main effect of the cornea remodelinginvolves the smoothing of epithelium at the anterior surface of the eye,where the epithelium tends to grow thicker and fill in the dips of thecornea surface as created by refractive surgery. Epithelial smoothingcan result in regression following refractive surgery, and sometimesleads to induced high-order aberrations that are particularly strong forhigh myopia and hyperopia cases.

Certain techniques have been proposed for minimizing inducedpost-operative SA, including linear adjustment of the basis data andnomogram adjustments. Although such techniques can provide benefits topatients in need thereof, further improvements would be desirable.Embodiments of the present invention provide solutions to address suchoutstanding needs.

In a first aspect, embodiments of the present invention encompassmethods of evaluating a treatment table for use in an ophthalmologicrefractive surgery for a patient. Methods may include, for example,inputting a treatment table containing laser ablation instructions fortreating the patient into a treatment instructions module, determining asimulated ablation for the patient based on the laser ablationinstructions with a simulation ablation module, inputting a pupildimension of the patient into a pupil dimension module, and determiningan expected optical refraction for the patient based on the pupildimension and the simulated ablation with an expected optical refractionmodule, where the expected optical refraction for the patient isdependent on a sphere ophthalmic term characterized by a set of secondradial order polynomial terms, a cylinder ophthalmic term characterizedby the set of second radial order polynomial terms, and an axisophthalmic term characterized by the set of second radial orderpolynomial terms, and where the expected optical refraction profile isindependent of a piston ophthalmic term characterized by a zero radialorder polynomial term, an x-tilt ophthalmic term characterized by a setof first radial order polynomial terms, and a y-tilt ophthalmic termcharacterized by the set of first radial order polynomial terms. Methodsmay further include inputting an intended optical refraction for thepatient into an intended refraction module, where the intended opticalrefraction for the patient is dependent on a sphere ophthalmic term, acylinder ophthalmic term, and an axis ophthalmic term, and where theintended optical refraction profile is independent of a pistonophthalmic term, an x-tilt ophthalmic term, and a y-tilt ophthalmicterm. Additionally, methods may include evaluating the treatment tableby comparing the expected and intended optical refractions for thepatient with a comparison module. In some cases, the set of secondradial order polynomial terms includes a set of second radial orderZernike polynomial terms, the zero radial order polynomial term includesa zero radial order Zernike polynomial term, and the set of first radialorder polynomial terms includes a set of first radial order Zernikepolynomial terms. In some cases, the set of second radial orderpolynomial terms includes a set of second radial order Seidel powerseries terms, the zero radial order polynomial term includes a zeroradial order Seidel power series term, and the set of first radial orderpolynomial terms includes a set of first radial order Seidel powerseries terms. Optionally, the expected optical refraction and theintended optical refraction each correspond to a common plane. In someinstances, the expected optical refraction and the intended opticalrefraction each correspond to a corneal plane. In some instances, thepupil dimension of the patient corresponds to a wavefront diameterrelated to a wavescan of the patient. In some instances, the pupildimensional of the patient comprises a pupil diameter that is equivalentto the wavefront diameter. According to some embodiments, the pupildimension of the patient is a pupil diameter of about 4 mm. Methods mayalso include determining if a difference between the expected andintended optical refractions for the patient is within a pre-definedtolerance. Methods may also include qualifying the treatment table foruse in the ophthalmologic refractive surgery for the patient if thedifference between the expected and intended optical refractions iswithin the pre-defined tolerance. Some method may include disqualifyingthe treatment table for use in the ophthalmologic refractive surgery forthe patient if the difference between the expected and intended opticalrefractions is not within the pre-defined tolerance.

In another aspect, embodiments of the present invention encompasssystems for evaluating a treatment table for use in an ophthalmologicrefractive surgery for a patient. Exemplary systems may include atreatment instructions module that accepts a treatment table containinglaser ablation instructions for treating the patient, a simulationablation module having a tangible medium embodying machine-readable codethat determines a simulated ablation for the patient based on the laserablation instructions, a pupil dimension module that accepts a pupildimension of the patient, and an expected optical refraction modulehaving a tangible medium embodying machine-readable code that determinesan expected optical refraction for the patient based on the pupildimension and the simulated ablation, where the expected opticalrefraction for the patient is dependent on a sphere ophthalmic termcharacterized by a set of second radial order polynomial terms, acylinder ophthalmic term characterized by the set of second radial orderpolynomial terms, and an axis ophthalmic term characterized by the setof second radial order polynomial terms, and where the expected opticalrefraction profile is independent of a piston ophthalmic termcharacterized by a zero radial order polynomial term, an x-tiltophthalmic term characterized by a set of first radial order polynomialterms, and a y-tilt ophthalmic term characterized by the set of firstradial order polynomial terms. Systems may further include an intendedrefraction module that accepts an intended optical refraction for thepatient, where the intended optical refraction for the patient isdependent on a sphere ophthalmic term, a cylinder ophthalmic term, andan axis ophthalmic term, and where the intended optical refractionprofile is independent of a piston ophthalmic term, an x-tilt ophthalmicterm, and a y-tilt ophthalmic term. Additionally, systems may include acomparison module having a tangible medium embodying machine-readablecode that evaluates the treatment table by comparing the expected andintended optical refractions for the patient. In some systemembodiments, the set of second radial order polynomial terms includes aset of second radial order Zernike polynomial terms, the zero radialorder polynomial term includes a zero radial order Zernike polynomialterm, and the set of first radial order polynomial terms includes a setof first radial order Zernike polynomial terms. In some systems, theexpected optical refraction and the intended optical refraction eachcorrespond to a common plane. In some systems, the expected opticalrefraction and the intended optical refraction each correspond to acorneal plane. Exemplary systems may also include a validation modulehaving a tangible medium embodying machine-readable code that determinesif a difference between the expected and intended optical refractionsfor the patient is within a pre-defined tolerance, and a qualificationmodule having a tangible medium embodying machine-readable code thatqualifies the treatment table for use in the ophthalmologic refractivesurgery for the patient if the difference between the expected andintended optical refractions is within the pre-defined tolerance.

In another aspect, embodiments of the present invention encompass acomputer program product embodied on a tangible computer readable mediumthat includes computer code for inputting a treatment table containinglaser ablation instructions for treating the patient, computer code fordetermining a simulated ablation for the patient based on the laserablation instructions, computer code for inputting a pupil dimension ofthe patient, and computer code for determining an expected opticalrefraction for the patient based on the pupil dimension and thesimulated ablation, where the expected optical refraction for thepatient is dependent on a sphere ophthalmic term characterized by a setof second radial order polynomial terms, a cylinder ophthalmic termcharacterized by the set of second radial order polynomial terms, and anaxis ophthalmic term characterized by the set of second radial orderpolynomial terms, and where the expected optical refraction profile isindependent of a piston ophthalmic term characterized by a zero radialorder polynomial term, an x-tilt ophthalmic term characterized by a setof first radial order polynomial terms, and a y-tilt ophthalmic termcharacterized by the set of first radial order polynomial terms.Computer program products may also include computer code for inputtingan intended optical refraction for the patient, where the intendedoptical refraction for the patient is dependent on a sphere ophthalmicterm, a cylinder ophthalmic term, and an axis ophthalmic term, and wherethe intended optical refraction profile is independent of a pistonophthalmic term, an x-tilt ophthalmic term, and a y-tilt ophthalmicterm, and computer code for evaluating the treatment table by comparingthe expected and intended optical refractions for the patient with acomparison module. For some computer program products, the set of secondradial order polynomial terms includes a set of second radial orderZernike polynomial terms, the zero radial order polynomial term includesa zero radial order Zernike polynomial term, and the set of first radialorder polynomial terms includes a set of first radial order Zernikepolynomial terms. For some computer program products, the expectedoptical refraction and the intended optical refraction each correspondto a common plane. For some computer program products, the expectedoptical refraction and the intended optical refraction each correspondto a corneal plane. Exemplary computer program products may also includecomputer code for determining if a difference between the expected andintended optical refractions for the patient is within a pre-definedtolerance, and computer code for qualifying the treatment table for usein the ophthalmologic refractive surgery for the patient if thedifference between the expected and intended optical refractions iswithin the pre-defined tolerance.

It has been discovered that deconvolution techniques based on a corneasmoothing model can be used to obtain an ablation target or treatmentshape that induces little or no post-operative SA. In some instances,these ablation targets or treatment shapes can provide a post-operativeSA that is equal to or below a naturally occurring amount of SA.

Hence, embodiments of the present invention encompass systems andmethods for obtaining a modified ablation target that is capable ofeliminating, reducing, or minimizing a systematic trend inpost-operatively induced spherical aberration. In some cases, themodification of the target shape introduces only a small increase in therequired depth for the ablation. Hence, such techniques are helpful inproviding safe and effective treatments. In some cases, the modificationof the target shape may change the peripheral cornea profile, which canaffect the SA without changing the central refractive power.

In some instances, embodiments encompass techniques for determining avision treatment for an eye of a patient, which may include obtaining anoriginal target profile for the eye of the patient, obtaining a spatialdomain kernel filter (e.g. based on an inverse Fourier transform of aFourier domain noise filter), convolving the original target profilewith the spatial domain kernel filter, and determining the visiontreatment based on the convolved profile.

In one aspect, embodiments of the present invention encompass systemsand methods for determining a vision treatment for an eye of a patient.Exemplary techniques may include, for example, receiving, at an input,an original target profile for the eye of the patient, and convolvingthe original target profile with the spatial domain kernel filter. Thespatial domain kernel filter can be based on an inverse Fouriertransform of a Fourier domain noise filter. Techniques may also includedetermining the vision treatment based on the convolved profile.Optionally, techniques may include administering the treatment to thepatient. In some instances, the Fourier domain noise filter is based ona conjugate of a Fourier domain complex matrix. In some instances, theFourier domain noise filter is based on a modulus of a Fourier domaincomplex matrix. In some instances, the Fourier domain noise filter isbased on a conjugate of a Fourier domain complex matrix and a modulus ofthe Fourier domain complex matrix. According to some embodiments, theFourier domain noise filter is characterized by fraction having anumerator comprising a conjugate of a Fourier domain complex matrix anda denominator comprising a modulus of the Fourier domain complex matrix.In some cases, the Fourier domain complex matrix is characterized by theformula

${K\left( {k_{x},k_{y}} \right)} = \frac{1}{1 + \frac{\sigma^{2}\left( {k_{x}^{2} + k_{y}^{2}} \right)}{\left( {0.5\; {dL}} \right)^{2}}}$

where σ represents a diffusion coefficient, k_(x) and k_(y) representfrequency domain variables, and dL represents a mesh size. In somecases, σ has a value of 0.35 mm and dL has a value of 0.1 mm.Optionally, σ may have a value within a range from about 0.2 mm to about0.5 mm. In some cases, σ may have a value within a range from about 0.33mm to about 0.4 mm. Optionally, the denominator can be characterized bythe expression |K(k_(x), k_(y))|^(n), where n is an integer having avalue of 2 or more. In some instances, the denominator can becharacterized by the expression [|K(k_(x), k_(y))|^(n)+SNR²] where n isan integer having a value of 2 or more and SNR represents a signal tonoise ratio value. In some instances, the convolved profile includes atransition zone radius, and a method may further include zeroing theconvolved profile at locations outside of the transition zone radius. Insome instances, the original target profile may include an originalrefractive spherical equivalent value within a 4 mm diameter area, andthe convolved target profile may include a target refractive sphericalequivalent value within a 4 mm diameter area. Optionally, the method mayfurther include scaling the original refractive spherical equivalentwith the target refractive spherical equivalent value. Some methods mayalso include elevating the convolved profile so that a lowest point onthe convolved profile is zero or greater. In some instances, a convolvedprofile includes a transition zone radius, and methods may includeapplying a damping multiplier at or near the transition zone radius. Insome instances, the target shape includes an optical zone having aperiphery, and the convolution effects a change in the target shape nearthe periphery of the optical zone.

In another aspect, embodiments of the present invention encompasssystems for determining a vision treatment for an eye of a patient.Exemplary systems may include an input that receives an original targetprofile for the eye of the patient, and a convolution module thatconvolves the original target profile with a spatial domain kernelfilter. The spatial domain kernel filter can be based on an inverseFourier transform of a Fourier domain noise filter. Systems may alsoinclude a treatment generation or determination module that determinesthe vision treatment based on the convolved profile. In some instances,the Fourier domain noise filter is based on a conjugate of a Fourierdomain complex matrix. In some instances, the Fourier domain noisefilter is based on a modulus of a Fourier domain complex matrix.

In still another aspect, embodiments of the present invention encompasscomputer program products for determining a vision treatment for an eyeof a patient. An exemplary computer program product may be embodied on anon-transitory tangible computer readable medium, and may includecomputer code for receiving an original target profile for the eye ofthe patient, computer code for convolving the original target profilewith a spatial domain kernel filter, and computer code for determiningthe vision treatment based on the convolved profile. The spatial domainkernel filter may be based on an inverse Fourier transform of a Fourierdomain noise filter.

In one aspect, embodiments of the present invention encompass systemsand methods for determining a vision treatment for an eye of a patient.Exemplary methods include receiving, at an input, an original targetprofile for the eye of the patient, and obtaining a deconvolved targetprofile based on the original target profile and a low pass filter. Insome cases, the low pass filter is an optimized linear filter. Methodsmay also include obtaining a scale factor, where the scale factor isbased on a low order refraction measure of a test eye population and alow order refraction measure of a convolved test eye population profile.In some cases, the convolved test eye population profile is based on aconvolution of the test eye population profile. Methods may also includedetermining a scaled target profile based on the deconvolved targetprofile and the scale factor, and determining the vision treatment basedon the scaled target profile. In some cases, methods may includevalidating the scaled target profile. In some cases, the scale factorhas a value within a range from about 0.4 to about 0.8. In some cases,the scale factor has a value of about 0.7489. In some cases, the loworder refraction measure of the test eye population profile includes afirst manifest refraction spherical equivalent measure and the low orderrefraction measure of the convolved test eye population profile includesa second manifest refraction spherical equivalent measure. In somecases, the first manifest refraction spherical equivalent measure is a 4mm refraction measure and the second manifest refraction sphericalequivalent measure is a 4 mm refraction measure.

In another aspect, embodiments of the present invention encompassmethods for determining a vision treatment for an eye of a patient,where exemplary methods include receiving, at an input, an originaltarget profile for the eye of the patient, determining a first low orderrefraction measure based on the original target profile, obtaining adeconvolved target profile based on the original target profile and alow pass filter, determining a second low order refraction measure basedon the deconvolved target profile, determining a scale factor based on acomparison between the first and second low order refraction measures,determining a scaled target profile based on the deconvolved targetprofile and the scale factor, and determining the vision treatment basedon the scaled target profile. According to some embodiments, methods mayinclude validating the scaled target profile. In some embodiments, thefirst low order refraction measure includes a first manifest refractionspherical equivalent measure and the second low order refraction measureincludes a second manifest refraction spherical equivalent measure. Insome embodiments, the first manifest refraction spherical equivalentmeasure is a 4 mm refraction measure and the second manifest refractionspherical equivalent measure is a 4 mm refraction measure. In someembodiments, the first low order refraction measure includes a firstsphere measure and the second low order refraction measure includes asecond sphere measure. In some embodiments, the first low orderrefraction measure includes a first cylinder measure and the second loworder refraction measure includes a second cylinder measure.

In still another aspect, embodiments of the present invention encompassmethods of determining a vision treatment for an eye of a patient thatinclude receiving, at an input, an original target profile for the eyeof the patient, obtaining a first healed profile based on the originaltarget profile, obtaining a deconvolved target profile based on theoriginal target profile and a low pass filter, obtaining a second healedprofile based on the deconvolved target profile, determining a first loworder refraction measure based on the first healed profile, determininga second low order refraction measure based on the second healedprofile, determining a scale factor based on a comparison between thefirst and second low order refraction measures, determining a scaledtarget profile based on the deconvolved target profile and the scalefactor, and determining the vision treatment based on the scaled targetprofile. According to some embodiments, methods may include validatingthe scaled target profile. In some instances, the first low orderrefraction measure includes a first manifest refraction sphericalequivalent measure and the second low order refraction measure includesa second manifest refraction spherical equivalent measure. In someinstances, the first manifest refraction spherical equivalent measure isa 4 mm refraction measure and the second manifest refraction sphericalequivalent measure is a 4 mm refraction measure. In some instances, thefirst low order refraction measure includes a first sphere measure andthe second low order refraction measure includes a second spheremeasure. In some instances, the first low order refraction measureincludes a first cylinder measure and the second low order refractionmeasure includes a second cylinder measure.

In yet another aspect, embodiments of the present invention encompassmethods of determining a vision treatment for an eye of a patient thatinclude receiving, at an input, an original target profile for the eyeof the patient, and obtaining a deconvolved target profile based on theoriginal target profile and a low pass filter. Some methods may includeobtaining a scale factor, where the scale factor is based on a low orderrefraction measure of a test eye population and a low order refractionmeasure of a convolved test eye population profile. In some cases, theconvolved test eye population profile is based on a convolution of thetest eye population profile. Methods may also include determining ascaled target profile based on the deconvolved target profile and thescale factor, adjusting a sphere parameter of the scaled target profilebased on a pre-operative cylinder measurement of the eye of the patient,and determining the vision treatment based on the adjusted targetprofile. According to some embodiments, methods may include validatingthe scaled target profile.

In still yet another aspect, embodiments of the present inventionencompass methods of determining a vision treatment for an eye of apatient that include receiving, at an input, a pre-operative cylindervalue for the eye of the patient, and determining the vision treatmentfor the eye, where the vision treatment includes a sphere value that isbased on the pre-operative cylinder value. In some cases, thepre-operative cylinder value is a manifest refraction measurement. Insome cases, the pre-operative cylinder value is a wavefront refractionmeasurement. In some cases, the sphere value of the vision treatment isdetermined based on the formula S=−0.2 C−0.25, where S is the spherevalue and C is the pre-operative cylinder value.

In another aspect, embodiments of the present invention encompassmethods of determining a vision treatment for an eye of a patient thatinclude receiving, at an input, an original target profile for the eyeof the patient, and obtaining a deconvolved target profile based on theoriginal target profile and a low pass filter. In some cases, the lowpass filter can be an optimized linear filter. Methods may also includeobtaining a scale factor, where the scale factor is based on a highorder aberration measure of a test eye population and a high orderaberration measure of a convolved test eye population profile. Theconvolved test eye population profile can be based on a convolution ofthe test eye population profile. Methods may also include determining ascaled target profile based on the deconvolved target profile and thescale factor, and adjusting a spherical aberration parameter of thescaled target profile based on a pre-operative spherical equivalentmeasurement (or a pre-operative sphere measurement) of the eye of thepatient, and determining the vision treatment based on the adjustedtarget profile. According to some embodiments, methods may includevalidating the adjusted target profile.

For a fuller understanding of the nature and advantages of the presentinvention, reference should be had to the ensuing detailed descriptiontaken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a laser ablation system according to an embodiment ofthe present invention.

FIG. 2 illustrates a simplified computer system according to anembodiment of the present invention.

FIG. 3 illustrates a wavefront measurement system according to anembodiment of the present invention.

FIG. 3A illustrates another wavefront measurement system according to anembodiment of the present invention.

FIG. 4 shows aspects of an evaluation system according to embodiments ofthe present invention.

FIG. 4A depicts aspects of an evaluation method according to embodimentsof the present invention.

FIG. 5 shows aspects of an evaluation system according to embodiments ofthe present invention.

FIG. 6 illustrates aspects of residual error according to embodiments ofthe present invention.

FIG. 7 illustrates aspects of residual sphere and cylinder according toembodiments of the present invention.

FIG. 8 depicts aspects of a method for determining a vision treatmentfor an eye, according to embodiments of the present invention.

FIG. 9 depicts aspects of a method for modifying a target shapeaccording to embodiments of the present invention.

FIG. 10A shows post-operative values and FIG. 10B shows aspects ofoptical and transition zones according to embodiments of the presentinvention.

FIG. 11 shows aspects of simulated epithelium thickness profilesaccording to embodiments of the present invention.

FIGS. 12A and 12B show aspects of flap SA and sigma relationshipsaccording to embodiments of the present invention.

FIGS. 13A to 13C depict aspects of post-operative SA and pre-operativeMRSE or SE relationships according to embodiments of the presentinvention.

FIGS. 14A and 14B illustrate aspects of spherical aberration errors fordeconvolution according to embodiments of the present invention.

FIGS. 15A and 15B show aspects of rescaling coefficients and refractionerrors, respectively, according to embodiments of the present invention.

FIGS. 16A and 16B depict aspects of effects of deconvolution on cylinderrefraction according to embodiments of the present invention.

FIGS. 16C and 16D illustrate aspects of ablation profile modificationsaccording to embodiments of the present invention.

FIGS. 17A to 17C depict aspects of pre-operative MRSE (ManifestRefraction Spherical Equivalent) according to embodiments of the presentinvention.

FIGS. 18A and 18B illustrate aspects of ablation profile modificationsaccording to embodiments of the present invention.

FIGS. 19A and 19B show aspects of pre-operative MRSE according toembodiments of the present invention.

FIGS. 20A and 20B show aspects of differences between modified targetsand original targets according to embodiments of the present invention.

FIG. 21 depicts aspects of shows post-operating secondary sphericalaberration according to embodiments of the present invention.

FIG. 22 depicts aspects of methods for generating a target shape,according to embodiments of the present invention.

FIG. 23 depicts aspects of relationships between RMS error and size of s(pixels), according to embodiments of the present invention.

FIG. 24 illustrates aspects of deconvolution methods according toembodiments of the present invention.

FIGS. 25A and 25B show aspects of ablation profile changes ormodifications according to embodiments of the present invention.

FIG. 26 illustrates aspects of induced SA according to embodiments ofthe present invention.

FIG. 27 illustrates aspects of deconvolution effects according toembodiments of the present invention.

FIG. 28 illustrates aspects of radial compensation function according toembodiments of the present invention.

FIG. 29 illustrates aspects of target shape modification according toembodiments of the present invention.

FIG. 30 shows aspects of induced SA according to embodiments of thepresent invention.

FIG. 31 illustrates aspects of low pass filter according to embodimentsof the present invention.

FIGS. 32A and 32B illustrate aspects of kernel and inverse kernelaccording to embodiments of the present invention.

FIG. 33 illustrates aspects of treatment target deconvolution accordingto embodiments of the present invention.

FIG. 34 depicts aspects of target verification according to embodimentsof the present invention.

FIGS. 35A to 35C illustrate aspects of residual error with deconvolutionaccording to embodiments of the present invention.

FIG. 36 depicts aspects of expected and inversed convolved targetsaccording to embodiments of the present invention.

FIG. 37 illustrates aspects of low pass filter according to embodimentsof the present invention.

FIG. 38 illustrates aspects of post-operative SA according toembodiments of the present invention.

FIG. 39 shows aspects of vision condition cases according to embodimentsof the present invention.

FIG. 40 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 41 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 42 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 43 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 44 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 45 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 46 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 46A illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 47 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 48 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 49 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 50 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 51 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 52 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 53 illustrates aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 53A depicts aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 53B depicts aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 53C depicts aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 54 depicts aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 55 depicts aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 56 depicts aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 57 depicts aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

FIG. 58 depicts aspects of treatment validation systems and methodsaccording to embodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the present invention encompass systems and methods fortreatment validation based on the preservation of low order aberrations.In some cases, a vision treatment for an eye of a patient can bedetermined by receiving an original target profile for the eye of thepatient, obtaining a deconvolved target profile based on the originaltarget profile and a low pass filter, such as an optimized linearfilter, determining a scaled target profile based on the deconvolvedtarget profile and a scale factor, and determining the vision treatmentbased on the scaled target profile. The scale factor can be based on alow order refraction measure of a test eye population and a low orderrefraction measure of a convolved test eye population profile, and theconvolved test eye population profile can be based on a convolution ofthe test eye population profile. In some cases, a vision treatment canbe determined by receiving an original target profile for the eye of thepatient, determining a first low order refraction measure based on theoriginal target profile, obtaining a deconvolved target profile based onthe original target profile and a low pass filter, determining a secondlow order refraction measure based on the deconvolved target profile,determining a scale factor based on a comparison between the first andsecond low order refraction measures, determining a scaled targetprofile based on the deconvolved target profile and the scale facto, anddetermining the vision treatment based on the scaled target profile. Insome cases, a vision treatment can be determined by receiving anoriginal target profile for the eye of the patient, obtaining a firsthealed profile based on the original target profile, obtaining adeconvolved target profile based on the original target profile and alow pass filter, obtaining a second healed profile based on thedeconvolved target profile, determining a first low order refractionmeasure based on the first healed profile, determining a second loworder refraction measure based on the second healed profile, determininga scale factor based on a comparison between the first and second loworder refraction measures, determining a scaled target profile based onthe deconvolved target profile and the scale factor, and determining thevision treatment based on the scaled target profile.

Embodiments of the present invention also emcompass systems and methodsfor treatment validation based on on sphere-cylinder coupling. Forexample, a vision treatment can be determined by receiving an originaltarget profile for the eye of the patient, obtaining a deconvolvedtarget profile based on the original target profile and a low passfilter, determining a scaled target profile based on the deconvolvedtarget profile and a scale factor, adjusting a sphere parameter of thescaled target profile based on a pre-operative cylinder measurement ofthe eye of the patient, and determining the vision treatment based onthe adjusted target profile. In some cases, the scale factor can bebased on a low order refraction measure of a test eye population and alow order refraction measure of a convolved test eye population profile,and the convolved test eye population profile can be based on aconvolution of the test eye population profile. In another example, avision treatment ca be determined by receiving a pre-operative cylindervalue for the eye of the patient, and determining the vision treatmentfor the eye, such that the vision treatment includes a sphere value thatis based on the pre-operative cylinder value.

Embodiments of the present invention encompass further systems andmethods for treatment validation based on techniques involving highorder aberrations, such as spherical aberration. For example, a visiontreatment can be determined by receiving an original target profile forthe eye of the patient, obtaining a deconvolved target profile based onthe original target profile and a low pass filter, such as an optimizedlinear filter, determining a scaled target profile based on thedeconvolved target profile and a scale factor, adjusting a sphericalaberration parameter of the scaled target profile based on apre-operative sphere (or a pre-operative spherical equivalent)measurement of the eye of the patient, and determining the visiontreatment based on the adjusted target profile. In some cases, the scalefactor can be based on a high order aberration measure of a test eyepopulation and a high order aberration measure of a convolved test eyepopulation profile, and the convolved test eye population profile can bebased on a convolution of the test eye population profile.

Embodiments of the present invention include systems and methods whichuse treatment table content (e.g. laser pulse instructions) to derive orgenerate an expected optical refraction, and compare that expectedrefraction with an intended refraction for the patient Typically,optical refractions include sphere, cylinder, and axis components. Inaddition to the treatment table laser instructions, the derived expectedrefraction may also take into account the treatment or vertex plane, forexample to ensure that the derived refraction plane matches the intendedrefraction plane. Further, embodiments of the present invention providesystems and methods for treatment table validation that implement aseparate, independent set of code to ensure that a planned refraction inthe treatment table is consistent with the desired refraction. Thus, anexemplary method may involve inputting an intended refraction for apatient, inputting a treatment table containing laser ablationinstructions, calculating an expected optical refraction based on thetreatment table and optionally a vertex or treatment plane parameter,comparing the expected optical refraction with the intended refraction,and evaluating the treatment table based on the comparison of theexpected optical refraction with the input refraction. If the expectedoptical refraction deviates significantly from the intended refraction,the treatment table will be disqualified.

In some cases, an intended optical refraction is dependent uponophthalmic sphere, cylinder, and axis terms that are not based onZernike values, whereas an expected optical refraction is dependent onsphere, cylinder, and axis terms that are based on Zernike values.Intended optical refractions, such as those dependent on ophthalmicsphere, cylinder, and axis terms, can be related to Zernikes (e.g.wavefront-guided), or physician input (e.g. VSS Refractive™ technique,non-wavefront guided, or manifest refraction). Optionally,wavefront-guided or nonwavefront-guided data can be used on conjunctionwith a physician adjustment.

Embodiments of the present invention can be readily adapted for use withexisting laser systems and other optical treatment devices. Althoughsystem, software, and method embodiments of the present invention aredescribed primarily in the context of a laser eye surgery system, itshould be understood that embodiments of the present invention may beadapted for use in or in combination with alternative eye treatmentprocedures, systems, or modalities, such as spectacle lenses,intraocular lenses, accommodating IOLs, contact lenses, corneal ringimplants, collagenous corneal tissue thermal remodeling, corneal inlays,corneal onlays, other corneal implants or grafts, and the like.Relatedly, systems, software, and methods according to embodiments ofthe present invention are well suited for customizing any of thesetreatment modalities to a specific patient. Thus, for example,embodiments encompass custom preformed lenses, intraocular lenses,custom contact lenses, custom corneal implants, and the like, which canbe configured to treat or ameliorate any of a variety of visionconditions in a particular patient based on their unique ocularcharacteristics or anatomy. Additionally, the modified ablation targetor target shape may be implemented via other non-ablative lasertherapies, such as laser-incised custom lenticule shapes and subsequentextraction and laser-based corneal incision patterns.

Exemplary systems and methods disclosed herein can be implemented via avariety of ophthalmic devices or solutions. For example, treatmenttechniques may be used for any of a variety of surgery modalities,including excimer laser surgery, femtosecond surgery, and the like. Avariety of forms of lasers and laser energy can be used to effect acorrection or treatment, including infrared lasers, ultraviolet lasers,femtosecond lasers, wavelength multiplied solid-state lasers, and thelike. By way of non limiting example, ophthalmic corrections can involvea cornea or lens reshaping procedure, such as, for example using apicosecond or femtosecond laser. Laser ablation procedures can remove atargeted amount stroma of a cornea to change a cornea's contour andadjust for aberrations. In some cases, a treatment protocol can involvethe delivery of a series of discrete pulses of laser light energy, witha total shape and amount of tissue removed being determined by a shape,size, location, and/or number of laser energy pulses impinging on orfocused within a cornea. In some cases, a surgical laser, such as anon-ultraviolet, ultra-short pulsed laser that emits radiation withpulse durations as short as nanoseconds and femtoseconds (e.g., afemtosecond laser, or a picosecond laser) can be used to treat the eyeof a patient. Other pulse widths may be suitable as well. The lasersystems can be configured to deliver near infrared light. Otherwavelengths may be used as well. The laser systems can be configured todeliver laser light focused at a focus depth (e.g. within corneal orother ophthalmologic tissue) which may be controlled by the system.Laser surgery with ultra-short pulse lasers such as femtosecond laserscan be used to treat the eye. These pulsed lasers can make very accurateincisions of the eye and can be used in many ways to treat the eye.Additional types of incisions that can be performed with the short pulselasers include incisions for paracentesis, limbal relaxing incisions,and refractive incisions to shape the cornea, for example.

In some cases, vision treatments can include focusing femtosecond laserenergy within the stroma so as to ablate a volume of intrastromaltissue. By scanning the focal spot within an appropriate volume of thestromal tissue, it is possible to vaporize the volume so as to achieve adesired refractive alteration. Hence, embodiments of the presentinvention encompass laser surgical techniques that involve femtosecondlaser photodisruption or photoalteration treatments. In some cases, afemtosecond laser can be used to perform the photodisruption, thusproviding an easy, precise, and effective approach to refractive surgery

According to some embodiments, a femtosecond laser (or other laser) ofthe optical system can be used to incise the cornea or to cut a flap. Afemtosecond laser may be used to make arcuate or other incisions in thecornea, which incisions may be customized, intrastromal, stable,predictable, and the like. Likewise, corneal entry incisions may bemade, which are custom, multi-plane, and self-sealing.

Pulsed laser beams include bursts or pulses of light. Pulsed lasers,such as non-ultraviolet, ultra-short pulsed lasers with pulse durationsmeasured in the nanoseconds to femtoseconds range, can be used inophthalmic surgical procedures as disclosed herein. For example, apulsed laser beam can be focused onto a desired area of ophthalmologicmaterial or tissue, such as the cornea, the capsular bag, or the lens ofthe eye, to photoalter the material in this area and, in some instances,the associated peripheral area. Examples of photoalteration of thematerial include, but are not necessarily limited to, chemical andphysical alterations, chemical and physical breakdown, disintegration,ablation, photodisruption, vaporization, a the like. Exemplary treatmentsystems can include a focusing mechanism (e.g. lens) and/or a scanningmechanism so as to guide or direct a focus of femtosecond energy along apath within the patient's eye.

In some instances, these techniques can be carried out in conjunctionwith treatments provided by any of a variety of laser devices, includingwithout limitation the WaveScan® System and the STAR S4® Excimer LaserSystem both by Abbott Medical Optics Inc., the WaveLight® AllegrettoWave® Eye-Q laser, the Schwind Amaris™ lasers, the 217P excimerworkstation by Technolas PerfectVision GmbH, the Mel 80™ laser by CarlZeiss Meditec, Inc., and the like. In some cases, embodiments providetechniques for using laser basis data during refractive surgerytreatment procedures which can be implemented in such laser devices.

Turning now to the drawings, FIG. 1 illustrates a laser eye surgerysystem 10 of the present invention, including a laser 12 that produces alaser beam 14. Laser 12 is optically coupled to laser delivery optics16, which directs laser beam 14 to an eye E of patient P. A deliveryoptics support structure (not shown here for clarity) extends from aframe 18 supporting laser 12. A microscope 20 is mounted on the deliveryoptics support structure, the microscope often being used to image acornea of eye E.

Laser 12 generally comprises an excimer laser, ideally comprising anargon-fluorine laser producing pulses of laser light having a wavelengthof approximately 193 nm. Laser 12 will preferably be designed to providea feedback stabilized fluence at the patient's eye, delivered viadelivery optics 16. The present invention may also be useful withalternative sources of ultraviolet or infrared radiation, particularlythose adapted to controllably ablate the corneal tissue without causingsignificant damage to adjacent and/or underlying tissues of the eye.Such sources include, but are not limited to, solid state lasers andother devices which can generate energy in the ultraviolet wavelengthbetween about 185 and 205 nm and/or those which utilizefrequency-multiplying techniques. Hence, although an excimer laser isthe illustrative source of an ablating beam, other lasers may be used inthe present invention.

Laser system 10 will generally include a computer or programmableprocessor 22. Processor 22 may comprise (or interface with) aconventional PC system including the standard user interface devicessuch as a keyboard, a display monitor, and the like. Processor 22 willtypically include an input device such as a magnetic or optical diskdrive, an internet connection, or the like. Such input devices willoften be used to download a computer executable code from a tangiblestorage media 29 embodying any of the methods of the present invention.Tangible storage media 29 may take the form of a floppy disk, an opticaldisk, a data tape, a volatile or non-volatile memory, RAM, or the like,and the processor 22 will include the memory boards and other standardcomponents of modern computer systems for storing and executing thiscode. Tangible storage media 29 may optionally embody wavefront sensordata, wavefront gradients, a wavefront elevation map, a treatment map, acorneal elevation map, and/or an ablation table. While tangible storagemedia 29 will often be used directly in cooperation with an input deviceof processor 22, the storage media may also be remotely operativelycoupled with processor by means of network connections such as theinternet, and by wireless methods such as infrared, Bluetooth, or thelike.

Laser 12 and delivery optics 16 will generally direct laser beam 14 tothe eye of patient P under the direction of a computer 22. Computer 22will often selectively adjust laser beam 14 to expose portions of thecornea to the pulses of laser energy so as to effect a predeterminedsculpting of the cornea and alter the refractive characteristics of theeye. In many embodiments, both laser beam 14 and the laser deliveryoptical system 16 will be under computer control of processor 22 toeffect the desired laser sculpting process, with the processor effecting(and optionally modifying) the pattern of laser pulses. The pattern ofpulses may by summarized in machine readable data of tangible storagemedia 29 in the form of a treatment table, and the treatment table maybe adjusted according to feedback input into processor 22 from anautomated image analysis system in response to feedback data providedfrom an ablation monitoring system feedback system. Optionally, thefeedback may be manually entered into the processor by a systemoperator. Such feedback might be provided by integrating the wavefrontmeasurement system described below with the laser treatment system 10,and processor 22 may continue and/or terminate a sculpting treatment inresponse to the feedback, and may optionally also modify the plannedsculpting based at least in part on the feedback. Measurement systemsare further described in U.S. Pat. No. 6,315,413, the full disclosure ofwhich is incorporated herein by reference.

Laser beam 14 may be adjusted to produce the desired sculpting using avariety of alternative mechanisms. The laser beam 14 may be selectivelylimited using one or more variable apertures. An exemplary variableaperture system having a variable iris and a variable width slit isdescribed in U.S. Pat. No. 5,713,892, the full disclosure of which isincorporated herein by reference. The laser beam may also be tailored byvarying the size and offset of the laser spot from an axis of the eye,as described in U.S. Pat. Nos. 5,683,379, 6,203,539, and 6,331,177, thefull disclosures of which are incorporated herein by reference.

Still further alternatives are possible, including scanning of the laserbeam over the surface of the eye and controlling the number of pulsesand/or dwell time at each location, as described, for example, by U.S.Pat. No. 4,665,913, the full disclosure of which is incorporated hereinby reference; using masks in the optical path of laser beam 14 whichablate to vary the profile of the beam incident on the cornea, asdescribed in U.S. Pat. No. 5,807,379, the full disclosure of which isincorporated herein by reference; hybrid profile-scanning systems inwhich a variable size beam (typically controlled by a variable widthslit and/or variable diameter iris diaphragm) is scanned across thecornea; or the like. The computer programs and control methodology forthese laser pattern tailoring techniques are well described in thepatent literature.

Additional components and subsystems may be included with laser system10, as should be understood by those of skill in the art. For example,spatial and/or temporal integrators may be included to control thedistribution of energy within the laser beam, as described in U.S. Pat.No. 5,646,791, the full disclosure of which is incorporated herein byreference. Ablation effluent evacuators/filters, aspirators, and otherancillary components of the laser surgery system are known in the art.Further details of suitable systems for performing a laser ablationprocedure can be found in commonly assigned U.S. Pat. Nos. 4,665,913,4,669,466, 4,732,148, 4,770,172, 4,773,414, 5,207,668, 5,108,388,5,219,343, 5,646,791 and 5,163,934, the complete disclosures of whichare incorporated herein by reference. Suitable systems also includecommercially available refractive laser systems such as thosemanufactured and/or sold by Alcon, Bausch & Lomb, Nidek, WaveLight,LaserSight, Schwind, Zeiss-Meditec, and the like. Basis data can befurther characterized for particular lasers or operating conditions, bytaking into account localized environmental variables such astemperature, humidity, airflow, and aspiration.

FIG. 2 is a simplified block diagram of an exemplary computer system 22that may be used by the laser surgical system 10 of the presentinvention. Computer system 22 typically includes at least one processor52 which may communicate with a number of peripheral devices via a bussubsystem 54. These peripheral devices may include a storage subsystem56, comprising a memory subsystem 58 and a file storage subsystem 60,user interface input devices 62, user interface output devices 64, and anetwork interface subsystem 66. Network interface subsystem 66 providesan interface to outside networks 68 and/or other devices, such as thewavefront measurement system 30.

User interface input devices 62 may include a keyboard, pointing devicessuch as a mouse, trackball, touch pad, or graphics tablet, a scanner,foot pedals, a joystick, a touchscreen incorporated into the display,audio input devices such as voice recognition systems, microphones, andother types of input devices. User input devices 62 will often be usedto download a computer executable code from a tangible storage media 29embodying any of the methods of the present invention. In general, useof the term “input device” is intended to include a variety ofconventional and proprietary devices and ways to input information intocomputer system 22.

User interface output devices 64 may include a display subsystem, aprinter, a fax machine, or non-visual displays such as audio outputdevices. The display subsystem may be a cathode ray tube (CRT), aflat-panel device such as a liquid crystal display (LCD), a projectiondevice, or the like. The display subsystem may also provide a non-visualdisplay such as via audio output devices. In general, use of the term“output device” is intended to include a variety of conventional andproprietary devices and ways to output information from computer system22 to a user.

Storage subsystem 56 can store the basic programming and data constructsthat provide the functionality of the various embodiments of the presentinvention. For example, a database and modules implementing thefunctionality of the methods of the present invention, as describedherein, may be stored in storage subsystem 56. These software modulesare generally executed by processor 52. In a distributed environment,the software modules may be stored on a plurality of computer systemsand executed by processors of the plurality of computer systems. Storagesubsystem 56 typically comprises memory subsystem 58 and file storagesubsystem 60.

Memory subsystem 58 typically includes a number of memories including amain random access memory (RAM) 70 for storage of instructions and dataduring program execution and a read only memory (ROM) 72 in which fixedinstructions are stored. File storage subsystem 60 provides persistent(non-volatile) storage for program and data files, and may includetangible storage media 29 (FIG. 1) which may optionally embody wavefrontsensor data, wavefront gradients, a wavefront elevation map, a treatmentmap, and/or an ablation table. File storage subsystem 60 may include ahard disk drive, a floppy disk drive along with associated removablemedia, a Compact Digital Read Only Memory (CD-ROM) drive, an opticaldrive, DVD, CD-R, CD-RW, solid-state removable memory, and/or otherremovable media cartridges or disks. One or more of the drives may belocated at remote locations on other connected computers at other sitescoupled to computer system 22. The modules implementing thefunctionality of the present invention may be stored by file storagesubsystem 60.

Bus subsystem 54 provides a mechanism for letting the various componentsand subsystems of computer system 22 communicate with each other asintended. The various subsystems and components of computer system 22need not be at the same physical location but may be distributed atvarious locations within a distributed network. Although bus subsystem54 is shown schematically as a single bus, alternate embodiments of thebus subsystem may utilize multiple busses.

Computer system 22 itself can be of varying types including a personalcomputer, a portable computer, a workstation, a computer terminal, anetwork computer, a control system in a wavefront measurement system orlaser surgical system, a mainframe, or any other data processing system.Due to the ever-changing nature of computers and networks, thedescription of computer system 22 depicted in FIG. 2 is intended only asa specific example for purposes of illustrating one embodiment of thepresent invention. Many other configurations of computer system 22 arepossible having more or less components than the computer systemdepicted in FIG. 2.

Referring now to FIG. 3, one embodiment of a wavefront measurementsystem 30 is schematically illustrated in simplified form. In verygeneral terms, wavefront measurement system 30 is configured to senselocal slopes of a gradient map exiting the patient's eye. Devices basedon the Hartmann-Shack principle generally include a lenslet array tosample the gradient map uniformly over an aperture, which is typicallythe exit pupil of the eye. Thereafter, the local slopes of the gradientmap are analyzed so as to reconstruct the wavefront surface or map.

More specifically, one wavefront measurement system 30 includes an imagesource 32, such as a laser, which projects a source image throughoptical tissues 34 of eye E so as to form an image 44 upon a surface ofretina R. The image from retina R is transmitted by the optical systemof the eye (e.g., optical tissues 34) and imaged onto a wavefront sensor36 by system optics 37. The wavefront sensor 36 communicates signals toa computer system 22′ for measurement of the optical errors in theoptical tissues 34 and/or determination of an optical tissue ablationtreatment program. Computer 22′ may include the same or similar hardwareas the computer system 22 illustrated in FIGS. 1 and 2. Computer system22′ may be in communication with computer system 22 that directs thelaser surgery system 10, or some or all of the components of computersystem 22, 22′ of the wavefront measurement system 30 and laser surgerysystem 10 may be combined or separate. If desired, data from wavefrontsensor 36 may be transmitted to a laser computer system 22 via tangiblemedia 29, via an I/O port, via an networking connection 66 such as anintranet or the Internet, or the like.

Wavefront sensor 36 generally comprises a lenslet array 38 and an imagesensor 40. As the image from retina R is transmitted through opticaltissues 34 and imaged onto a surface of image sensor 40 and an image ofthe eye pupil P is similarly imaged onto a surface of lenslet array 38,the lenslet array separates the transmitted image into an array ofbeamlets 42, and (in combination with other optical components of thesystem) images the separated beamlets on the surface of sensor 40.Sensor 40 typically comprises a charged couple device or “CCD,” andsenses the characteristics of these individual beamlets, which can beused to determine the characteristics of an associated region of opticaltissues 34. In particular, where image 44 comprises a point or smallspot of light, a location of the transmitted spot as imaged by a beamletcan directly indicate a local gradient of the associated region ofoptical tissue.

Eye E generally defines an anterior orientation ANT and a posteriororientation POS. Image source 32 generally projects an image in aposterior orientation through optical tissues 34 onto retina R asindicated in FIG. 3. Optical tissues 34 again transmit image 44 from theretina anteriorly toward wavefront sensor 36. Image 44 actually formedon retina R may be distorted by any imperfections in the eye's opticalsystem when the image source is originally transmitted by opticaltissues 34. Optionally, image source projection optics 46 may beconfigured or adapted to decrease any distortion of image 44.

In some embodiments, image source optics 46 may decrease lower orderoptical errors by compensating for spherical and/or cylindrical errorsof optical tissues 34. Higher order optical errors of the opticaltissues may also be compensated through the use of an adaptive opticelement, such as a deformable mirror (described below). Use of an imagesource 32 selected to define a point or small spot at image 44 uponretina R may facilitate the analysis of the data provided by wavefrontsensor 36. Distortion of image 44 may be limited by transmitting asource image through a central region 48 of optical tissues 34 which issmaller than a pupil 50, as the central portion of the pupil may be lessprone to optical errors than the peripheral portion. Regardless of theparticular image source structure, it will be generally be beneficial tohave a well-defined and accurately formed image 44 on retina R.

In one embodiment, the wavefront data may be stored in a computerreadable medium 29 or a memory of the wavefront sensor system 30 in twoseparate arrays containing the x and y wavefront gradient valuesobtained from image spot analysis of the Hartmann-Shack sensor images,plus the x and y pupil center offsets from the nominal center of theHartmann-Shack lenslet array, as measured by the pupil camera 51 (FIG.3) image. Such information contains all the available information on thewavefront error of the eye and is sufficient to reconstruct thewavefront or any portion of it. In such embodiments, there is no need toreprocess the Hartmann-Shack image more than once, and the data spacerequired to store the gradient array is not large. For example, toaccommodate an image of a pupil with an 8 mm diameter, an array of a20×20 size (i.e., 400 elements) is often sufficient. As can beappreciated, in other embodiments, the wavefront data may be stored in amemory of the wavefront sensor system in a single array or multiplearrays.

While the methods of the present invention will generally be describedwith reference to sensing of an image 44, it should be understood that aseries of wavefront sensor data readings may be taken. For example, atime series of wavefront data readings may help to provide a moreaccurate overall determination of the ocular tissue aberrations. As theocular tissues can vary in shape over a brief period of time, aplurality of temporally separated wavefront sensor measurements canavoid relying on a single snapshot of the optical characteristics as thebasis for a refractive correcting procedure. Still further alternativesare also available, including taking wavefront sensor data of the eyewith the eye in differing configurations, positions, and/ororientations. For example, a patient will often help maintain alignmentof the eye with wavefront measurement system 30 by focusing on afixation target, as described in U.S. Pat. No. 6,004,313, the fulldisclosure of which is incorporated herein by reference. By varying aposition of the fixation target as described in that reference, opticalcharacteristics of the eye may be determined while the eye accommodatesor adapts to image a field of view at a varying distance and/or angles.

The location of the optical axis of the eye may be verified by referenceto the data provided from a pupil camera 52. In the exemplaryembodiment, a pupil camera 52 images pupil 50 so as to determine aposition of the pupil for registration of the wavefront sensor datarelative to the optical tissues.

An alternative embodiment of a wavefront measurement system isillustrated in FIG. 3A. The major components of the system of FIG. 3Aare similar to those of FIG. 3. Additionally, FIG. 3A includes anadaptive optical element 53 in the form of a deformable mirror. Thesource image is reflected from deformable mirror 98 during transmissionto retina R, and the deformable mirror is also along the optical pathused to form the transmitted image between retina R and imaging sensor40. Deformable mirror 98 can be controllably deformed by computer system22 to limit distortion of the image formed on the retina or ofsubsequent images formed of the images formed on the retina, and mayenhance the accuracy of the resultant wavefront data. The structure anduse of the system of FIG. 3A are more fully described in U.S. Pat. No.6,095,651, the full disclosure of which is incorporated herein byreference.

The components of an embodiment of a wavefront measurement system formeasuring the eye and ablations may comprise elements of a WaveScan®system, available from AMO MANUFACTURING USA, LLC, MILPITAS, California.One embodiment includes a WaveScan system with a deformable mirror asdescribed above. An alternate embodiment of a wavefront measuring systemis described in U.S. Pat. No. 6,271,915, the full disclosure of which isincorporated herein by reference. It is appreciated that any wavefrontaberrometer could be employed for use with the present invention.Relatedly, embodiments of the present invention encompass theimplementation of any of a variety of optical instruments provided byAMO WaveFront Sciences, LLC, including the COAS wavefront aberrometer,the ClearWave contact lens aberrometer, the CrystalWave IOL aberrometer,and the like.

Relatedly, embodiments of the present invention encompass theimplementation of any of a variety of optical instruments provided byWaveFront Sciences, Inc., including the COAS wavefront aberrometer, theClearWave contact lens aberrometer, the CrystalWave IOL aberrometer, andthe like. Embodiments of the present invention may also involvewavefront measurement schemes such as a Tscherning-based system, whichmay be provided by WaveFront Sciences, Inc. Embodiments of the presentinvention may also involve wavefront measurement schemes such as a raytracing-based system, which may be provided by Tracey Technologies,Corp.

FIG. 4 depicts aspects of an evaluation system 400 according toembodiments of the present invention. As shown here, system 400 mayinclude an Input Refraction module 412, a Wavefront module 422, aZernike Reconstruction module 424, a Wavefront Refraction module 426, aPhysician Adjustment module 432, a Nomogram Adjustment module 434, anIntended Refraction module 436, a Treatment Instructions module 442, aPupil Dimension module 443, a Simulated Ablation module 444, a ZernikeDecomposition module 446, an Expected Refraction module 448, and aComparison module 452.

Input Refraction

The Input Refraction module 412 can operate to receive, process, andtransmit information related to original refractions from the patient,such as VSS Refractive™ technology (Variable Spot Scanning) data, ormanifest or subjective refraction. This information can correspond tonon-wavefront guided data. According to some embodiments, InputRefraction module 412 can be configured to receive information regardingthe refractive error of a patient. Such refractive error information mayinclude sphere, cylinder, cylinder axis, and vertex distance data.Hence, low order aberration information can be used. For example,refractive error information may correspond to input cases such asmyopia or hyperopia. In some cases, the refractive error information maybe obtained at or correlated with a spectacle plane (e.g. 12.5 mmvertex). Input Refraction module 412 can also be configured to convertthe input refractive error information to refractive error informationrelative to the corneal plane. Such plane conversion techniques arediscussed in G.-m. Dai, Wavefront Optics for Vision Correction (SPIEPress, 2008), which is incorporated herein by reference. Planeconversion techniques can correspond to a vertex distance change oradjustment. Embodiments of the present invention encompass systems andmethods for converting between treatment planes, user-defined orphysician-defined planes, spectacle planes, corneal planes, pupilplanes, and other planes of interest. Further, Input Refraction module412 can be configured to output or transmit the corneal plane refractiveerror information, which may include sphere, cylinder, cylinder axis,and vertex distance components. In some cases, the refractive errorinformation can be presented in the following format: sphere valueDS/cylinder value DC x axis value @ vertex distance value. Optionally,Sphere and Cylinder can be represented in terms of diopters of power,Axis can be represented in terms of angle or degrees, and VertexDistance can be represented in terms of millimeters. Sphere typicallypresents a measurement of lens power for myopia (negative) or hyperopia(positive), and cylinder typically presents a measurement of lens powerfor astigmatism. Hence, this refraction information and other eyemeasurements can be processed, as described herein, and compared withprocessed treatment table information to qualify the treatment table.

Wavefront

The Wavefront module 422 can operate to receive, process, and transmitinformation related to CustomVue™ technology or wavefront guided data.According to some embodiments, Wavefront module 422 can be configured toreceive information regarding the wavefront error of a patient. Suchwavefront error information may include wavefront map and wavefrontdiameter data. In some cases, the wavefront error information may beobtained at or correlated with a pupil plane. Wavefront module 422 canalso be configured to process Hartmann-Shack spot diagram data, forexample as described in G.-m. Dai, Wavefront Optics for VisionCorrection (SPIE Press, 2008). Hartmann-Shack data can correspond towavefront map data and wavefront diameter data. Typically,Hartmann-Shack data provides x and y shift information corresponding toarray lenslets, and a wavefront data map can be derived from theHartmann-Shack data. The map may optionally be associated with aparticular wavefront diameter, particularly when the map is describedwith Zernike terms. In some cases, the map may be represented by adiscrete matrix. Hence, Wavefront module 422 can be configured to outputor transmit wavefront slope data, which may include x- and y-slopeinformation.

Zernike Reconstruction

The Zernike Reconstruction module 424 can operate to receive informationsuch as wavefront slope data, including for example x- and y-slope data.Zernike Reconstruction module 424 can also be configured to process thewavefront slope data with a Zernike reconstruction technique to obtainZernike coefficient data, for example as described in G.-m. Dai,Wavefront Optics for Vision Correction (SPIE Press, 2008). Further,Zernike Reconstruction module 424 can be configured to output ortransmit the Zernike coefficient information.

Wavefront Refraction

The Wavefront Refraction module 426 can operate to receive Zernikecoefficient information, such as data related to z3, z4, and z5 Zernikecoefficients. Wavefront Refraction module 426 can also be configured toreceive wavefront diameter information. What is more, WavefrontRefraction module 426 can be configured to determine or calculatewavefront refraction information, for example based on Zernikecoefficients and wavefront diameter, as discussed in G.-m. Dai,Wavefront Optics for Vision Correction (SPIE Press, 2008). The wavefrontrefraction information can be generated so as to correlated with a pupilplane, or with a corneal plane. Further, Wavefront Refraction module 426can transmit or output the wavefront refraction information.

Physician Adjustment

The Physician Adjustment module 432 can be configured to receiveinformation related to additional refractive correction at the uservertex or plane which may be selected or desired by a physician oroperator. The selected plane can correspond to the pupil plane, thecornea plane, the spectacle plane, or some other user-defined plane. ThePhysician Adjustment can be applied at the selected or user-definedplane. For example, if the user vertex or plane corresponds to aspectacle plane, the physician can apply the adjustment at the spectacleplane as well. Hence, if the physician desired to add another diopter oftreatment, the additional diopter could be applied at the spectacleplane when the physician is planning for a particular treatment. Theadjustment is combined with the correction, and the combination can beconverted to another plane, for example the corneal plane. PhysicianAdjustment module 432 can also be configured to convert the physicianadjustment to the corneal plane, as described in G.-m. Dai, WavefrontOptics for Vision Correction (SPIE Press, 2008). Moreover, PhysicianAdjustment module 432 can be configured to transmit or outputinformation relating the physician adjustment at the corneal plane. Suchinformation corresponding to the corneal plane, or another selectedplane, can be used for comparison and evaluation as discussed elsewhereherein.

Nomogram Adjustment

The Nomogram Adjustment module 434 can be configured to receiveinformation related to a percentage of a treatment target multiplicationfactor. Nomogram Adjustment module 434 can also be configured tomultiply the nomogram factor. The multiplication factor can bedetermined by the sum of one plus the nomogram adjustment percentage.For example, if the nomogram adjustment percentage is 8%, themultiplication factor can be calculated as one plus 8/100, or 1.08.According to some embodiments, the nomogram adjustment percentage can bea value within a range from about −10% to about +10%. Relatedly,according to some embodiments, the multiplication factor can be a valuewithin a range from about 0.9 to about 1.1. Further, the NomogramAdjustment module 434 can be configured to transmit or outputinformation corresponding to a multiplied treatment target.

Intended Refraction

The Intended Refraction module 436 can operate to receive informationdirectly from Wavefront Refraction module 426, or from PhysicianAdjustment module 432 or Nomogram Adjustment module 434. According tosome embodiments, Intended Refraction module 436 can be configured toreceive information that is similar to or the same as the inputrefraction discussed above in relation to the Input Refraction module412. For example, Intended Refraction module 436 can be configured toreceive information regarding the refractive error of a patient. Suchrefractive error information may include sphere, cylinder, cylinderaxis, and vertex distance data. In some cases, the refractive errorinformation may be obtained at or correlated with a spectacle plane.Typically, the refractive error information or intended refractioninformation is based on a correction that is planned for application tothe patient's eye. Such intended or desired refractive correctioninformation can also be represented in terms of ocular or opticalrefraction data. Intended Refraction module 436 can also be configuredto convert the input refractive error information to refractive errorinformation relative to the corneal plane. Such plane conversiontechniques are discussed in G.-m. Dai, Wavefront Optics for VisionCorrection (SPIE Press, 2008). Further, Intended Refraction module 436can be configured to output or transmit the corneal plane refractiveerror information, which may include sphere, cylinder, cylinder axis,and vertex distance components. For example, Intended Refraction module436 can be configured to transmit refractive information that isdependent upon or correlated with a sphere ophthalmic term, a cylinderophthalmic term, and an axis ophthalmic term.

In some cases, the intended optical refraction can be related to Zerniketerms, and in some cases the intended optical refraction can be relatedto manifest refraction which is used in VSS refractive. For example, theintended optical refraction can be dependent upon ophthalmic terms suchas sphere, cylinder, and axis that are not directly related to Zerniketerms. In some instances, the resolution of a wavefront aberrometerdevice may be greater than that of a phoropter device. Hence, a patientreceiving a wavefront aberrometer exam that provides a result of 3.75diopters, may also receive a phoropter exam that provides a result of3.50 diopters. Either of the wavefront or manifest refraction resultsmay be used.

Treatment Instructions

The Treatment Instructions module 442 can be configured to receiveinformation related to a treatment target. Further, TreatmentInstructions module 442 can operate to process the treatment targetinformation according to a simulated annealing least squares algorithm(SALSA) to obtain a treatment table or set of laser ablationinstructions for a patient, as described in G.-m. Dai, Wavefront Opticsfor Vision Correction (SPIE Press, 2008). The treatment table mayinclude laser instruction parameters such as iris size, x- andy-scanning positions or locations, shot-to-shot or beam pulse delaytime, pulse or beam size, and other ablation instruction parameters. Thelaser parameters can be used to deliver an ablation that corresponds tothe Zernike polynomial terms, or other basis function terms such asSeidel series terms. A refraction typically corresponds to a secondorder polynomial, and basic functions such as Zernike polynomials andSeidel series are well suited for characterizing refractions based oncalculation of second order coefficients. Treatment Instructions module442 may also be configured to transmit or output laser ablationinstructions, such as iris size, x- and y-scanning positions,shot-to-shot delay time, and the like. The treatment table maycharacterize information that has been processed via a table generationengine. When the ablation is simulated based on the ensemble of laserinstructions, the resulting volumetric information corresponds to theZernike terms.

A laser treatment table can include, for example, a listing ofcoordinate references for delivery of a laser beam during an ablation ofthe cornea. In some cases, a treatment table includes the value of thediscrete radial and angular positions of the optomechanical elementsused to scan an image over a portion of the anterior corneal surface.Treatment tables may also contain laser pulse instructions such as size,location, sequence, and the number of laser pulses per position. Inorder to provide a patient with an effective, predictable, and safesurgical procedure, it is important to generate and implement atreatment table which is accurate.

Pupil Dimension

The Pupil Dimension module 443 can operate to process informationrelated to a pupil dimension of the patient. In some cases, PupilDimension module 443 can be configured to receive a selected wavefrontor pupil diameter, and to calculate a refraction corresponding to thepupil dimension. Such information can be transmitted to a ZernikeDecomposition module, as discussed elsewhere herein. In some cases, apupil diameter can correspond with a wavefront diameter used during awavefront exam, for example a wavefront exam which may be performed inconjunction with the operation of Wavefront module 422. The pupildimension may in some instances have a value within a range from about 3mm to about 7 mm. In some cases, the pupil dimension is a pupil diameterof about 4 mm. Hence, embodiments encompass techniques that calculate arefraction over a 4 mm pupil diameter, as well as other pupildimensions. Exemplary aspects of pupil dimension selection are discussedin U.S. Pat. No. 7,460,288, which is incorporated herein by reference.

Simulated Ablation

The Simulated Ablation module 444 can be configured to receiveinformation related to laser ablation instructions, such as iris size,x- and y-scanning positions or tracking distances, shot-to-shot delaytime, and the like. Simulated Ablation module 444 can also be configuredto process information related to a simulated laser ablation or laserablation instructions to obtain a simulated volume or tissue volumeplanned for removal, based on basis data. Often, specific basis datainformation is available for corresponding specific iris sizes. Hence,for each particular iris size there can be a corresponding basis datainformation. Further, Simulated Ablation module 444 can be configured tooutput or transmit the simulated volume or tissue volume intended to beremoved.

Zernike Decomposition

The Zernike Decomposition module 446 can be configured to receiveinformation related to a pupil dimension and a tissue volume beingremoved. Zernike Decomposition module 446 can also be configured toprocess the pupil dimension and tissue volume information according to asingular value decomposition method to obtain Zernike coefficient andwavefront diameter information. In some cases, Zernike Decompositionmodule 446 generates data related to a set of second radial orderZernike polynomial terms. The second order Zernike polynomials, z3 z4,and z5 are analytically related to sphere, cylinder, and axis. The groupof z3 z4, and z5 terms can be used to determine sphere. Similarly, thegroup of z3 z4, and z5 terms can be used to determine cylinder. Further,the group of z3 z4, and z5 terms can be used to determine axis. Aspectsof a singular value decomposition method are discussed in G.-m. Dai,Wavefront Optics for Vision Correction (SPIE Press, 2008). Further,Zernike Decomposition module 446 can be configured to transmit or outputinformation related to the Zernike coefficients and wavefront diameter.As discussed elsewhere herein, embodiments may encompass techniques thatinvolve other basis function coefficients or second order radialpolynomials, for example Seidel power series.

Expected Refraction

The Expected Refraction module 448 can be configured to receiveinformation regarding Zernike coefficients (e.g. z3, z4, and z5 terms)and a pupil dimension. Expected Refraction module 448 can be configuredto determine a wavefront refraction based on the Zernike coefficient andpupil dimension information. Aspects of a wavefront refractiondetermination are discussed in G.-m. Dai, Wavefront Optics for VisionCorrection (SPIE Press, 2008). Further, Expected Refraction module 448can be configured to transmit or output information related to anexpected optical refraction for the patient, which may include forexample a sphere ophthalmic term characterized by a set of second radialorder Zernike polynomial terms, a cylinder ophthalmic term characterizedby the set of second radial order Zernike polynomial terms, and an axisophthalmic term characterized by the set of second radial order Zernikepolynomial terms. Optical refraction information typically correspondsto second order wavefront data or low order aberrations, and isdistinctly different from a surface shape, height, or topography. Forexample, when piston is added, the surface shape changes, however thecurvature or refraction does not. Similarly, if a surface is tilted, thesurface changes, however the curvature or refraction does not. Pistoncorresponds to a zero order Zernike polynomial, and represents upward ordownward displacement of a wavefront. Relatedly, tilt corresponds to afirst order Zernike polynomial.

Comparison

The Comparison module 452 can operate to compare intended refractioninformation with expected optical refraction information. For example,intended spherical equivalent (which corresponds to sphere and cylinder)can be compared with expected spherical equivalent, intended cylindercan be compared with expected cylinder, and intended axis can becompared with expected axis. In some cases, Comparison module 452 can beconfigured to receive information regarding an intended refraction andan expected or achieved refraction, optionally adjusted to orcharacterized in terms of a common or user-defined plane such as thecorneal plane, pupil plane, or spectacle plane.

Because refractions are typically dependent upon the vertex plane, itmay be desirable to compare intended and expected optical refractioninformation that corresponds to a common or specific vertex plane.Exemplary vertex or refraction conversions which may be used aredescribed in U.S. Pat. No. 7,296,893, incorporated herein by reference.Hence, if the input refraction data corresponds to the spectacle plane,and the wavefront data corresponds to the pupil plane, embodiments ofthe present invention encompass techniques for converting this data sothat it may be compared with data corresponding to a common plane, suchas the corneal plane. Comparison module 452 can also be configured tocompare the intended refraction and expected optical refractioninformation. For example, Comparison module 452 can operate to determinean algebraic difference for the sphere, cylinder, and axis ophthalmicterms, and compare the differences with a tolerance for the ophthalmicterm. Comparison module 452 can also be configured to qualify ordisqualify a treatment table based on the comparison between therespective refraction differences and tolerances.

Typically, comparison module 452 operates to compare low orderaberration information related to the intended refraction with low orderaberration information related to the expected refraction. Embodimentsof the present invention also encompass techniques that involve thecomparison of high order aberration information related to the intendedrefraction with high order aberration information related to theexpected refraction.

Hence, comparison techniques can involve comparing an expected opticalrefraction for the patient, which is based on a pupil dimension and asimulated ablation, with an intended optical refraction for the patient.The expected optical refraction can be dependent on a sphere ophthalmicterm characterized by a set of second radial order Zernike polynomialterms, a cylinder ophthalmic term characterized by the set of secondradial order Zernike polynomial terms, and an axis ophthalmic termcharacterized by the set of second radial order Zernike polynomialterms. The expected optical refraction profile can also be independentof a piston ophthalmic term characterized by a zero radial order Zernikepolynomial term, an x-tilt ophthalmic term characterized by a set offirst radial order Zernike polynomial terms, and a y-tilt ophthalmicterm characterized by the set of first radial order Zernike polynomialterms. The intended optical refraction for the patient can be dependenton a sphere ophthalmic term, a cylinder ophthalmic term, and an axisophthalmic term. Further, the intended optical refraction profile can beindependent of a piston ophthalmic term, an x-tilt ophthalmic term, anda y-tilt ophthalmic term.

Scaling

With continued reference to FIG. 4, evaluation techniques can beimplemented in various ways. For example, in a VSS refractive treatment,an evaluation technique may be implemented by using a scaling factor toscale down the refraction from the treatment table, without using ascaling factor to boost the treatment target. Such approaches are wellsuited for use with a Munnerlyn shape which is deeper than a parabolicshape. Relatedly, in a CustomVue® treatment, an evaluation technique maybe implemented by using a scaling factor, for example of 1.11, to boostthe treatment target, without using a scaling factor to scale down therefraction from the treatment table, for example without a parabolic orMunnerlyn scaling. With regard to the VSS technique, scaling can beapplied in a linear fashion, to a Munnerlyn or parabolic shape. In somecase, a Munnerlyn shape can be scaled so as to approach or approximate aparabolic shape. A parabolic shape represents a second order shape, anda Munnerlyn represents a second order shape as supplemented with higherorders. Hence, for the same refraction, a Munnerlyn shape and aparabolic shape can differ. A comparison can be performed either at thecorneal plane or at the vertex plane, or both. According to someembodiments, the treatment table should qualify or pass if thedifference between the refraction from the table and the initial inputrefraction is smaller than the criteria used for wavefront examselection during the treatment table creation phase. In some cases,embodiments of the present invention provide systems and methods forqualifying a VSS refractive treatment. Exemplary techniques canimplement a treatment qualification validation process whereby arefraction from a simulated tissue ablation is compared with an inputrefraction, for example to ensure that no abnormal tables have beencreated. Because the Munnerlyn shape and a parabolic shape may differ,it may be useful to convert a Munnerlyn refraction to a parabolicrefraction. Munnerlyn shapes are discussed generally at C. R. Munnerlyn,S. J. Koons, and J. Marshall, “Photorefractive keratectomy: A techniquefor laser refractive surgery,” J. Cataract Refract. Surg. 14, 46-52(1988), the entire content of which is incorporated herein by reference.Embodiments of the present invention encompass different types ofscaling. For example, the techniques disclosed herein may includerefraction scaling or shape scaling, both of which involvemultiplication. In some cases, it is possible to use scaling factors of1.015 for myopic sphere, 1.025 for hyperopic sphere, and 1.015 forcylinder to scale a refraction, for example as discussed in relation toEqs. (9) to (11) provided elsewhere herein. In some cases, it ispossible to use a scaling factor of 1.11 to scale a shape.

FIG. 4A illustrates an exemplary method 400 a of evaluating a treatmenttable for use in an ophthalmologic refractive surgery for a patient. Asshown here, such evaluation, verification, or qualification techniquesmay include inputting a treatment table containing laser ablationinstructions for treating the patient, as depicted by step 410 a.Methods may also include determining a simulated ablation for thepatient based on the laser ablation instructions as indicated by step420 a, and inputting a pupil dimension of the patient as indicated bystep 430 a. In an exemplary embodiment, an evaluation method may includedetermining an expected optical refraction for the patient based on thepupil dimension and the simulated ablations, as indicated by step 440 a,wherein the expected optical refraction for the patient is dependent ona sphere ophthalmic term characterized by a set of second radial orderZernike polynomial terms, a cylinder ophthalmic term characterized bythe set of second radial order Zernike polynomial terms, and an axisophthalmic term characterized by the set of second radial order Zernikepolynomial terms. Optionally, the expected optical refraction profilecan be independent of a piston ophthalmic term characterized by a zeroradial order Zernike polynomial term, an x-tilt ophthalmic termcharacterized by a set of first radial order Zernike polynomial terms,and a y-tilt ophthalmic term characterized by the set of first radialorder Zernike polynomial terms. Method embodiments may also includeinputting an intended optical refraction for the patient, as indicatedby step 450 a, wherein the intended optical refraction for the patientis dependent on a sphere ophthalmic term, a cylinder ophthalmic term,and an axis ophthalmic term, and wherein the intended optical refractionprofile is independent of a piston ophthalmic term, an x-tilt ophthalmicterm, and a y-tilt ophthalmic term. Further, methods may includecomparing the expected and intended optical refractions for the patient,as indicated by step 460 a. The refractions can be adjusted to orcorrelated with a common plane, such as the treatment plane, pupilplane, corneal plane, or spectacle plane, prior to the comparison. Insome cases, methods may include evaluating the treatment table based onthe comparison between the expected and intended optical refractions forthe patient, as indicated by step 470 a, and qualifying or disqualifyingthe treatment table based on the evaluation, as indicated by step 480 a.For example, evaluation methods may include determining a differencebetween the intended optical refraction and the expected opticalrefraction, and comparing that difference to a predefined tolerance. Ifthe difference between the intended optical refraction and the expectedoptical refraction is within the tolerance, the method may includequalifying or passing the treatment table, or otherwise approving thetreatment table for use. Such qualification techniques can provide anenhanced level of safety during a patient treatment, for example byhelping to ensure that a treatment table has not been altered or hacked.

Information corresponding to any of a variety of inputs may beprocessed, such as data related to a spectacle plane parameter, acorneal plane, a pupil plane, or any other desired vertex plane ordistance parameter.

FIG. 5 depicts aspects of an evaluation system 500 according toembodiments of the present invention. As shown here, system 500 mayinclude a Table Generation DLL module 510, a Treatment Validation DLLmodule 520, a Treatment Table module 530, an Independent TableValidation module 540, and a Final Table module 550.

As shown here, for a Table Generation DLL 510 or treatment generationengine, a validation process can be performed by a Treatment ValidationDLL 520 whereby a validation is conducted for various possiblesimulation annealing solutions. Moreover, a process to validate aready-to-use treatment corresponding to Treatment Table 530 can providea separate, independent step for validating a treatment table. Such anindependent validation technique can operate separately from a treatmenttable generation engine or a treatment table generation algorithm whichmay involve a simulated annealing process, and therefore does notincorporate possible error which may result, for example, due tounexpected error from third-party DLLs, from mal-operation of the usersthat is not captured in the fault tree analysis during the softwaredesign phase, or from other possible sources of error. For example, dueto possible unknown bugs or errors in the high level software code orembedded in third-party libraries (DLLs), or due to inappropriateoperation of the software, it is possible that a software that isverified and validated by Treatment Validation DLL 520 may still producean unwanted treatment table that can potentially result in a suboptimaltreatment. Hence, embodiments of the present invention encompassvalidation techniques for addressing situations where third partycomponents such as operating systems, computers, or DLL's introduceerror or are malfunctioning, and other sources that introduceunforeseeable or incorrect results.

According to some embodiments, the validation of a treatment table canbe implemented in connection with the table generation system orsoftware. In some cases, the validation of a treatment table can beimplemented in connection with the laser system or software, such asvalidation software residing in the laser system. For instance, aVSS-based validation as described elsewhere herein, which may optionallybe in relation with an aberrometer or wavefront system, can also beimplemented in a laser system. Hence, it is possible to validate atreatment table after it is generated and saved, and it is also possibleto validate a treatment table prior to use in treating a patient. Hence,if a treatment table has been corrupted for some reason, validation andqualification can be performed prior to laser delivery of the ablationpulses, and the treatment can be canceled if disqualification isappropriate.

According to some embodiments, the validation of a treatment table canbe implemented in connection with software residing in a diagnosticdevice such as WaveScan® and iDesign™ devices. System and methodembodiments disclosed herein can also be configured to validatetreatment tables for topographic driven treatment, refraction driven orconventional treatment, and wavefront driven treatment.

Table Generation DLL module 510 can operate to process informationrelated to treatment table generation, Treatment Validation DLL module520 can operate to process information related to treatment validation,Treatment Table module 530 can operate to process information related toa treatment table, and Table Validation module 540 can operate toprocess information related to table validation. In some instances,Table Validation module 540 is configured to embody or implementtechniques described elsewhere herein in relation to Comparison module452. Final Table module 550 can operate to process information relatedto a final table. According to some embodiments, a final tablecorresponding to Final Table module 550 will be the same as a treatmenttable corresponding to Treatment Table module 530, in the event that thetreatment table corresponding to Treatment Table module 530 is validatedor qualified by Table Validation module 540.

Passing Criteria for Treatment Table Qualification

Any of a variety of exam selection criteria can be used to qualify atreatment table generated by the VSS Refractive™ technique. NumerousMonte Carlo simulations have been performed which support thesuitability of such exam selection criteria for treatment tablequalification.

According to some embodiments, the difference in spherical equivalent(SE), cylinder, and cylinder angle can be set or predetermined tosatisfy the following qualification conditions.

|dSE|=|dS+0.5dC|=|S ₁ −S ₀+0.5C ₁−0.5C ₀|<0.625  (1)

|dC|=|C ₁ −C ₀|≦0.5  (2)

|dA|≦−1.1538(|C ₀ |+|C ₁|)/2+15.577(for |C ₀|>0.5 and |C ₁|>0.5, orignore)  (3)

As described here, Eq. 1 represents a comparison or difference betweenspherical equivalent, Eq. 2 represents a comparison or differencebetween cylinder, and Eq. 3 represents a comparison or differencebetween axis.

For example, if C₀=0.55 D, C₁=0.5 D, then according to Eq. 1, thecylinder difference is less than 0.5, and thus there may be no need tocheck cylinder angle. For another example, if C₀=0.9 D, C₁=0.8 D, thendA must be smaller than 14.6 degree in order to qualify. Also note thatfor Eq. (2), it is generally desirable that both use the same cylindernotation before the difference can be taken. For example, it isdesirable that both C₀ and C₁ be positive, or that both C₀ and C₁ benegative.

Evaluation and Monte Carlo Simulation

Treatment qualification systems and methods according to embodiments ofthe present invention can be implemented in a variety of ways. There istypically inter-correlation between sphere and cylinder as well as thevertex correction. A scaling factor between a Munnerlyn power and aparabolic power may in some cases depend not only upon the sphererefraction, but also upon on the cylinder refraction. As described inG.-m. Dai, Wavefront Optics for Vision Correction (SPIE Press, 2008),the Munnerlyn shape may differ from a parabolic shape. For example, asdescribed at page 90, supra, the Munnerlyn shape can be 11% deeper thanparabolic shape, when a spherical myopia is considered.

Embodiments of the present invention encompass empirically adjusted andtheoretically based systems and methods for implementing a treatmentqualification technique. Such approaches can include processing a set ofinput refractions (e.g. with sphere between −15 D and +7 D and cylinderbetween −6 D and +6 D) with Munnerlyn shapes, decomposing the data intoZernike polynomials. Zernike decomposition may involve processing pupildimension and tissue volume information to obtain Zernike coefficientand wavefront diameter information, such as data related to a set ofsecond radial order Zernike polynomial terms, and determining therefractions based on the Zernike information. In this way, it ispossible to determine an expected refraction, based on the Zernikecoefficient and pupil dimension information.

Further, these approaches can include regressing the input Munnerlynrefraction against a calculated parabolic refraction using multivariatelinear and quadratic parameters to obtain theoretical scaling factorsfor both sphere and cylinder. Still further, these approaches caninclude using a theoretical algorithm to test in a full implementationwith vertex correction, cosine effect using random keratometry values,and the like, using Monte Carlo simulation with multiple (e.g. 5000)samples. Moreover, these approaches can include refining the theoreticalalgorithm based on the Monte Carlo simulation. What is more, theseapproaches can include retesting the revised algorithm for a new set ofMonte Carlo simulation with multiple (e.g. 5000) samples. According tosome embodiments, such approaches may be implemented in a productionsoftware.

The following formulas give an algorithm for sphere (f_(s)) and cylinder(f_(c)) scaling:

f _(s)=1.028−0.00275S−0.00448C(S<0)  (4)

f _(s)=1.028−0.00326S−0.00018C(S≧0)  (5)

f _(c)=1.011−0.00574S−0.00142C  (6)

As indicated here, both S and C can be refractions on the corneal plane.In some cases, it may be desirable to convert the input refractions onvertex plane to the corneal plane before these equations are used.Supposing the refractions on the vertex plane are S₀ and C₀,respectively, it is possible to write:

$\begin{matrix}{S = \frac{S_{0}}{1 - {0.001\; S_{0}d}}} & (7) \\{C = {\frac{S_{0} + C_{0}}{1 - {0.001\left( {S_{0} + C_{0}} \right)d}} - S}} & (8)\end{matrix}$

When f_(s) and f_(c) are calculated, they can be applied to refractionson the corneal plane. For example, suppose the input refractions are −15DS/−5.75 DC×64 @ 12.5 mm vertex. They are used to generate the Munnerlynshape, which has more power than the corresponding parabolic shape. FromEquations (7) and (8), it is possible to obtain the refractions on thecorneal plane as −12.63 DS/−3.84 DC×64 @ 0 mm vertex. Using Equations(4) and (6), it is possible to obtain f_(s)=1.0799 and f_(c)=1.0889.These are scaling factors which may be determined via Monte Carlosimulation. Further, such scaling factors can be applied to an inputrefraction. It can be assumed that the Zernike decomposed refractionsfrom the treatment table are −13.68 DS/−4.09 DC×64 @ 0 mm vertex.

According to some embodiments, for the CustomVue® technique or Wavefrontinput data, there may be no need to use a scaling factor forrefractions, however it may be beneficial to scale the treatment shape11% to achieve a similar target depth corresponding to that ofconventional or VSS Refractive™ input data.

The scaling factors for these refractions can be applied to obtain−12.67 DS/−3.76 DC×64 @ 0 mm vertex, which may correspond to a scaledrefraction on the treatment plane or corneal plane. It is possible toconvert these refractions to a 12.5 mm vertex using Equations (7) and(8), setting d=−12.5 mm. Such conversion corresponds to propagation tothe spectacle plane. Hence, −12.67 DS/−3.76 DC×64 @ 0 mm vertexpropagated to the spectacle plane is −15.05 DS/−5.62 DC×64 @ 12.5 mmvertex. Conversions are useful when comparing refractions, such as anintended refraction and an expected refraction, and this exampleillustrates that it is possible to compare refractions in, for example,a user vertex (e.g. spectacle) plane. Hence, a treatment table power of−13.68/−4.09×64 at 0 mm vertex can be vertex corrected to obtain therefraction as −15.05DS/−5.62 DC×64 at 12.5 mm vertex. This leaves aresidual error of −0.05 DS/0.13 DC.

The difference in SE can be calculated as(−15.05−5.62/2+15+5.75/2)=0.02D, the difference in Cylinder can becalculated as −5.62+5.75=0.07D, and the difference in axis can becalculated as 0. If the tolerance for SE is 0.625D and the tolerance forcylinder is 0.5D, then these SE and Cylinder values are within thetolerances, and hence the treatment can be approved for release to treatthe patient.

FIG. 6 shows a residual error for 5000 simulated cases with 6 mm OZ. Theleft panel shows residual sphere, and the right panel shows residualcylinder, after correction of the scaling factors for 5000 simulatedrealistic cases. If the four outliers are excluded, the spread of sphereis within (−0.4D, +0.1D) and that of cylinder is within (−0.2D, +0.3D),both are in about half a diopter range. Without the exclusion, the rangeis still within the criteria listed in Eqs. (1) to (3).

Table 1 provides the residual error or residual refractions (indiopters) from a Monte Carlo simulation after implementing the algorithmshown in Eqs. (4) to (6), for optical zones of 7 mm, 6 mm, 5 mm, and 4mm.

TABLE 1 OZ 7 (mm) 6 (mm) 5 (mm) 4 (mm) Rx Sphere Cylinder SphereCylinder Sphere Cylinder Sphere Cylinder N 5000 5000 5000 5000 5000 50005000 5000 Mean −0.043 0.015 −0.043 0.014 −0.045 0.016 −0.013 0.017 Stdev0.054 0.044 0.054 0.044 0.057 0.047 0.045 0.035 Max 0.206 0.480 0.0900.476 0.149 0.432 0.132 0.265 Min −0.564 −0.330 −0.622 −0.215 −0.6100.245 −0.376 −0.171

For the criteria for treatment table qualification, because the residualerrors shown in Table 1 are within the exam selection criteria, it maybe desirable to use the exam selection criteria to qualify treatmenttables in terms of the refraction check. Embodiments of the presentinvention encompass techniques for qualifying an exam, which may involvethe application of treatment table qualification criteria, and selectingthe exam for treatment generation, which may involve the application ofexam selection criteria.

Verification with Production Code and Revised Formulas

Eqs. (4) to (6) were implemented in a production code, and tested withabout 1000 cases with each pupil sizes of 4 mm, 5 mm, 6 mm, and 7 mm.Occasional discrepancies were discovered, and it was determined thatsuch discrepancies may be due to some implementation differences betweenthe C++ code and the Matlab code. Subsequently, a set of new exampleswere generated and regression ran. Results for the new examples weremuch more linear, and the nonlinear behavior previously observed wasabsent.

Table 2 shows the linear factor for different pupil sizes. Scalingfactor data for sphere (t) and cylinder (f_(c)) was regressed from dataobtained with the production code for various pupil sizes.

TABLE 2 Pupil Minus Sph Plus Sph Cylinder 4 mm 0.999 1.022 1.010 5 mm1.014 1.037 1.023 6 mm 1.026 1.026 1.014 7 mm 1.023 1.014 1.014 Average1.015 1.025 1.015

Based on the information in Table 2, the original Eqs. (4) to (6) wereadjusted as follows. These equations can override equations (4)-(6).

f _(s)=1.015(S<0)  (9)

f _(s)=1.025(S>0)  (10)

f _(c)=1.015  (11)

As a verification that this new implementation narrows the spread of theresidual error both in sphere and cylinder, the same 5000 samples foreach pupil which were used before, were again used running with theproduction code. This is the revised code based on the adjustmentsdescribed above. FIG. 7 shows the results obtained for a 6 mm pupilusing the revised code, compared with the previous results obtainedusing the original code. Specifically, the upper panels of FIG. 7 showthe residual sphere (left panel) and residual cylinder (right panel) fora 6 mm pupil after correction of the scaling factors for 5000 simulatedrealistic cases using the original Eqs. (4) to (6). In comparison, thelower panels of FIG. 7 show the residual sphere (left panel) andcylinder (right panel) for a 6 mm pupil after correction of the scalingfactors for 5000 simulated realistic cases using the revised Eqs. (9) to(11). From FIG. 7, it can be seen that after the scaling factorrevision, the spread of the residual error in sphere and cylinderbecomes tighter. Therefore, in a normal condition, it is not expectedthat any treatment would fail. However, if a treatment does not satisfya validation test, it can be inferred that something unexpected may havehappened. In such instances, the treatment table can be disqualified,and the treatment will not be applied to the patient. Hence, thisexample illustrates that for validating treatment tables, a set ofnumerical formulas can be developed and validated with multiple MonteCarlo simulations of 5000 cases for each optical zone of 4, 5, 6, and 7mm.

Embodiments of the present invention encompass systems and methods forestimating or determining a scaling factor. Such techniques may involveconstructing a theoretical Munnerlyn shape for all refractive casescovered by the VSS Refractive™ technique (e.g. S and C with increment of0.25 D), calculating a decomposed refraction over a 4 mm diameter, andregressing using a multivariate quadratic regression model. Embodimentsmay also include calculating a wavefront refraction over a pupildimension (e.g. assuming the wavefront diameter is not smaller than thepupil dimension), and converting the refraction to a vertex distance.Embodiments may also include calculating a 2D Munnerlyn shape,decomposing a surface into Zernike coefficients, calculating Zernikepolynomials of each term, calculating Zernike polynomials of arbitrarysize and returning a 2-D surface mesh.

Embodiments of the present invention further encompass systems andmethods based on validation with a Monte Carlo Simulation. Exemplarytechniques may involve performing a validation using Monte Carlosimulation which ensures that implementation of a validation techniquepasses all regular cases within a proposed range, for example a proposed−15 to +7 DS and −6 to +6 DC range for the VSS Refractive™ procedure.Such approaches can be based on a proposed tolerance that is the same asor similar to a an exam qualification, such as 0.625 D for SE and 0.5 Dfor cylinder. For example, for a 6 mm optical zone (OZ) and 12.5 mmvertex, it is possible to input sphere, cylinder, and axis datacorresponding to a vertex plane, and sphere, cylinder, and axis datacorresponding to a corneal plane. Similarly, it is possible to outputsphere, cylinder, and axis data corresponding to a corneal plane.Embodiments also encompass determining scaling factors for sphere,cylinder, and axis, and calculating scaled sphere, cylinder, and axisvalues for corneal and vertex planes. Further, embodiments includedetermining differences between sphere, cylinder, and axis values at acorneal plane. A Monte Carlo simulation can be run with multiple (e.g.1000) random refractions. Embodiments include calculating a predictedrefraction versus a decomposed refraction from the treatment targets.Embodiments may also include calculating a refraction on the cornealplane. In some cases, embodiments encompass determining sphere andcylinder scaling factors. Embodiments may also include determining anempirical scaling factor for Munnerlyn power, where S and C representthe refraction on a corneal surface. Refractions can be converted to thecorneal plane, and scaling factors can be calculated based on cornealrefractions.

Post-Operative Aberrations

Refractive procedures may, in some cases, induce certain aberrations inan eye of a patient. For example, it is believed that laser-assisted insitu keratomileusis (LASIK) surgeries can induce high order aberrations,and in particular spherical aberration (SA). Spherical aberration is aspecial type of high order aberration that can affect night vision, andinvolves off-axis rays entering the eye with different heights of focusat different locations.

Embodiments of the present invention encompass systems and methods forreducing, eliminating, or otherwise compensating for such post-operativeinductions. For example, whereas an original target shape applied to theeye may lead to induced aberrations, it is possible to deconvolve theoriginal target shape so as to obtain a modified target shape, such thatwhen the modified target shape is applied to the eye, there are fewer orless pronounced induced aberrations.

FIG. 8 depicts aspects of a method 800 for determining a visiontreatment for an eye of a patient As shown here, the method includesreceiving (e.g. at an input) an original target profile for the eye ofthe patient as indicated by step 810. Method 800 also includes obtaininga spatial domain kernel filter as indicated by step 820. The spatialdomain kernel filter can be based on an inverse Fourier transform of aFourier domain noise filter. Further, the method may include convolvingthe original target profile with the spatial domain kernel filter asindicated by step 830. As illustrated here, method 800 also may includedetermining the vision treatment based on the convolved profile asindicated by step 840. According to some embodiments, methods mayinclude administering the vision treatment to the patient as indicatedby step 850.

FIG. 9 depicts aspects of a method for modifying a target shapeaccording to embodiments of the present invention. As shown here, amodification method 900 includes obtaining a target shape as indicatedby step 910. Often, the target shape or profile will have an opticalzone and a transition zone. In some cases, a target shape may refer toan intended optical surface designed to achieve a given refractivecorrection. A method 900 for modifying or deconvolving a target shapemay also include offsetting an inner boundary of the transition zone(e.g. by about 0.1 mm in diameter), as indicated by step 920. Further,the method may include inputting, receiving, or reading in an inversesmoothing kernel as described elsewhere herein. As illustrated by step930, methods may include applying a deconvolution to a target profile,for example as a low pass filter multiplied with the target profile asdiscussed below with reference to Equation 25. Methods may also includezeroing out an ablation profile at distances greater than the transitionzone radius, as indicated by step 940. In some cases, methods mayinclude rescaling a deconvolved target, for example as indicated by step950, so that its Zernike defocus term within the 4 mm diameter is thesame as for the original target. In some instances, the rescaling factorcan be 1.0. In some embodiments, the rescaling process described in step950 can incorporate scaling or rescaling techniques disclosed elsewhereherein, such as those described in FIGS. 22, 24, 41, and 42 and thecorresponding specification text descriptions. Optionally, methods mayinclude elevating the entire ablation profile, as depicted by step 960,so that the lowest point on the ablation profile is zero. This elevationtechnique can help to ensure that the ablation profile does not havenegative heights. In some instances, methods may include applying adamping multiplier (e.g. Equation 28) to the periphery of the transitionzone, as indicated by step 970. Optionally, a modification ordeconvolution method can be implemented before application of a cosinecompensation step.

Post-Operative Epithelial Smoothing And Spherical Aberration

As noted above, cornea remodeling following treatment with a refractivetarget shape can induce SA, for example due to smoothing of epitheliumat the anterior surface of the eye. To develop techniques thatcompensate for such remodeling, it is helpful to simulate thepost-operative epithelium smoothing process with a model. An exemplarymodel may define the shape of the post-operative cornea surface as aconvolution of an ablation target profile with a low-pass filter (LPF),as follows:

h _(post-op) =h _(pre-op) −K

T  Equation 12

where T is the ablation target profile. K=K(x,y) is the LPF kernel,which has the following

Fourier transform:

$\begin{matrix}{{K\left( {k_{x},k_{y}} \right)} = \frac{1}{1 + {\sigma^{2}\left( {k_{x}^{2} + k_{y}^{2}} \right)}}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

K(x,y), the LPF kernel, can be considered as a spatial domainrepresentation. The Fourier transform of K(x,y) (i.e. K(k_(x), k_(y)) orF[K]), can be considered as a frequency or Fourier domainrepresentation.

According to some embodiments, the Fourier transform F[K], or K(k_(x),k_(y)), may be a squared Butterworth low-pass filter of the first order,which can be applied to the treatment target Tin order to obtain thewavefront change due to corneal smoothing. In some instances, theFourier transform of the LPF kernel can be defined by or based on asingle diffusion coefficient σ, which has a unit of length.

In some instances, the post-operative induced spherical aberration canbe computed with a Zernike decomposition of the simulated post-operativecornea surface after the smoothing, as follows:

SA_(post-op)=SA_(pre-op)−SA(K

T)  Equation 14

The spherical aberration computed by Zernike decomposition of a giventarget can be represented by the function SA(T), where SA(T) refers toSA from the target T.

According to an exemplary experimental embodiment, a target for each eyein a clinical study was computed as follows:

T=scale·T _(controller)  Equation 15

According to some embodiments, T_(controller) may refer to a targetcreated by production code. Such a target can be created according tovarious options. For example, the target shape can be generated based oninput such as measured pre-operative Zernike coefficients with addedflap-induced spherical aberration (e.g. flapSA). The target shape canalso be generated with or without applying a cosine correction (e.g.warping adjustment). In some cases, the target can be generated based onscaling and/or physician adjustments. Target shapes may also begenerated based on keratometry parameters. For example, if available,keratometry parameters k1, k2, k2a may be used. Optionally, for exampleif keratometry parameters are not available, default values of k1=43.5,k2=43.5, k2σ=0 may be used.

It is possible to simulate the cornea thickness after smoothing using anLPF model. For example, FIG. 11 shows simulated epithelium thicknessprofiles after smoothing (High Myopia study, case ID=21011 OD,−7.4D/−1.5D×179). For this illustration, pre-operative epithelium wasassumed uniform and 50 um thick. Corneal smoothing after a myopicablation may lead to epithelium diffusion, from high curvature areas onthe peripheral transition zone, toward the center where the curvature issmaller. As a result, the epithelium may become thicker in the centerand thinner on the periphery of the ablation target. This effect mayhelp explain partial regression after myopia refractive surgery.

Using available clinical data, a smoothed target was compared with theobserved 6M corneal change within 6 mm and 5.5 mm diameter optical zone.A diffusion coefficient σ was estimated based on the comparison. In somecases, the comparison can be performed with a linear least-square fit ofthe model to the observed SA change, as described elsewhere herein.According to some embodiments, the fitting procedure yielded anestimation of σ and its confidence interval for each value of flapSA.

Various independent estimations of σ were used, including (a) RMS matchfor low and high Myopia (6M), (b) and Hyperopia (6M-9M), and (c)slope-based estimation for low Myopia (6M). For example, FIGS. 12A and12B depict optimized sigma vs. flap induced SA (simulations for clinicalstudies) for WFD=6 mm and WFD=5.5 mm, respectively. The dashed linesrepresent confidence intervals. WFD refers to a wavefront diameter.

As flap-induced aberrations typically do not depend on the type of thesubsequent treatment, it is possible to assume that the optimal valuesfor flapSA and σ can be chosen within the crossing of confidenceintervals for these three estimates (e.g. circled data points in FIGS.12A and 12B). These points can define optimal values approximately σ=0.3mm, flapSA=0.09 um for 6 mm wavefront and σ=0.45 mm, flapSA=0.05 um for5.5 mm wavefront. Some clinical observations for a flap incision withouta subsequent ablation show close values for the flap induced SA (e.g.flapSA≅0.07 um).

It is possible to compare simulated and observed post-operative SA (e.g.with WFD=6 mm). For example, as depicted in FIGS. 13A, B, and C, anestimated diffusion coefficient σ=0.3 mm for 6 mm wavefront diameter maybe validated by comparison of simulated post-operative operative SA withthe actual observed values. A flapSA=0.09 um was assumed for all datasets. In some embodiments, this value might be different for mechanicalmicrokeratome and IntraLase® femtosecond laser treatments. Asillustrated here, trend lines for simulated and observed data can bealmost identical for myopia and high myopia data and rather close forother data sets.

Hence, it is understood that epithelial smoothing subsequent torefractive surgery can induce SA, and that simulation of smoothing canbe helpful in developing approaches that compensate for the smoothing.In some cases, it is possible to define the shape of the post-operativecornea surface as a convolution of an ablation target profile with alow-pass filter (LPF).

In some cases, the post-operative epithelium smoothing process can besimulated by defining the shape of the post-operative cornea surface asa convolution of the ablation target profile with a low-pass filter(LPF) as follows (spatial domain):

h _(post-op) =h _(pre-op) −K(x,y)

T(x,y)  Equation 16

where h stands for the elevation maps,

denotes a convolution, T(x, y) is the ablation target profile and K(x,y) is a low pass filter (LPF) kernel, which has the following Fouriertransform:

$\begin{matrix}{{K\left( {k_{x},k_{y}} \right)} = \frac{1}{1 + \frac{\sigma^{2}\left( {k_{x}^{2} + k_{y}^{2}} \right)}{\left( {0.5\; {dL}} \right)^{2}}}} & {{Equation}\mspace{14mu} 17}\end{matrix}$

Equation 17, which is in the Fourier domain, represents a squaredButterworth low-pass filter of the first order, which can be applied tothe treatment target in order to obtain the wavefront change due to thecorneal smoothing. It can be defined by a single diffusion coefficientσ, which has a unit of length. For some discrete case embodiments, the101×101 mesh size can be dL=0.1 mm. Based on optimizations using datafrom certain clinical trials, a sigma of 0.35 mm was determined to bestexplain that observed data.

According to some embodiments, K(x, y) is in the spatial domain, and isa Fourier transform of K(k_(x), k_(y)). Here, k_(x) and k_(y) areFourier domain or frequency domain variables. According to someembodiments, K(x, y) is an LPF kernel that can be exemplified by a101×101 matrix or by a 3-D surface expressed in matrix form where x andy are spatial domain variables.

Matching Simulation Results Vs. Observed Data

According to some embodiments, it is possible to match or comparesimulated post-operative SA with observed 6M post-operative SA usinglinear least-square fit of the model to the observed SA change byminimizing the following function:

$\begin{matrix}{F = {\sum\limits_{{all}\_ {eyes}}^{\;}\; \frac{\begin{bmatrix}{{flapSA} + {{SA}\left( {K \otimes T} \right)} -} \\\left( {{SA}_{{post} - {op}} - {SA}_{{pre} - {op}}} \right)\end{bmatrix}^{2}}{N}}} & {{Equation}\mspace{14mu} 18}\end{matrix}$

Here SA_(pre-op) and SA_(post-op) are spherical aberration values forpre-operational and 6M post-operative wavefront measurements, flapSA isthe immediate flap-induced SA value before the smoothing, and N is thenumber of eyes. It is possible to compute this function (F) fordifferent flapSA and diffusion coefficients, σ, and for each flapSA tofind the value σ min where fitting residual is minimal. SA (K

T) refers to the SA of the target T after LPF.

The confidence interval for the optimized σ can be roughly estimated as:

$\begin{matrix}{{\Delta\sigma} = {\frac{{std}\left( \left\lbrack {{{SA}\left( {K \otimes T} \right)} - \left( {{SA}_{{post}\text{-}{op}} - {SA}_{{pre}\text{-}{op}}} \right)} \right\rbrack^{2} \right)}{\sqrt{N}} \cdot \frac{\sigma}{{SA}}}} & {{Equation}\mspace{14mu} 19}\end{matrix}$

Here std is a standard deviation, computed for the ensemble of eyes withthe optimized value σ=σ_(min.)

Both optimized σ and its confidence interval can depend on the value offlapSA. This dependence can be computed separately for myopic (6M) andhyperopic (6M-9M) eyes, for example as depicted in FIGS. 12A and 12B.Hence, it is possible to have two independent estimations for optimizedflapSA and σ.

An alternative estimation of these values can be obtained from matchingthe simulated vs. observed trend slopes, as follows:

$\begin{matrix}{{\langle\frac{{\Delta}\; {SA}^{({sim})}}{{SE}_{{pre}\text{-}{op}}}\rangle}_{all\_ eyes} = {\langle\frac{\Delta \; {SA}^{(\exp)}}{{SE}_{{pre}\text{-}{op}}}\rangle}_{all\_ eyes}} & {{Equation}\mspace{14mu} 20}\end{matrix}$

Here ΔSA=SA(K

T)−(SA_(post-op)−SA_(pre-op)). The optimized σ can provide a simulatedslope that is the same as the observed slope. A confidence interval forthis estimate can be defined as 95% confidence interval for the slope oflinear regression, as follows:

$\begin{matrix}{{\Delta\sigma} = {\frac{\sigma}{{SA}} \cdot \frac{t_{0.025} \cdot s}{s_{x}\sqrt{N - 1}}}} & {{Equation}\mspace{14mu} 21}\end{matrix}$

Here t_(0.025)=1.96,

${s^{2} = {\frac{N - 1}{N - 2} \cdot \left( {s_{y}^{2} - {s_{x}^{2}\frac{{SA}_{{post}\text{-}{op}}}{{SE}_{{pre}\text{-}{op}}}}} \right)}},$

s_(x)=stdev(SE_(pre-op)), s_(y)=stdev(SA_(post-op)). The slope-basedestimation was calculated for a Myopia study.

Offset Transition Zone

In some instances, a target shape or ablation target profile willinclude an optical zone and a transition zone. The aggregate of theoptical zone and transition zone may be referred to as an ablation zone,corresponding to the entire corneal region covered by a laser ablation.The optical zone may refer to a corneal region which received a fullintended refractive treatment. A transition zone may refer to a cornealregion outside of the optical zone but inside of the ablation zone.Often, a transition zone receives a treatment that is not strictlyoptically correct. With returning reference to FIG. 9, exemplary methodsmay also include offsetting an inner boundary of the transition zone, asindicated by step 920. According to some embodiments, an original targetshape may include a transition zone starting at about 0.25 mm inside theboundary of the optical zone. It is possible that such a target mayinduce some post-operative SA, independent of any effect corneasmoothing may have on post-operative SA. Hence, a total induced SA mayinclude a target-induced SA combined with a subsequent smoothing-inducedSA.

For example, FIG. 10A depicts post-operative values, in microns,simulated with σ=0.3 mm for study data (n=340), for SA as indicated inTable 3.

TABLE 3 Symbol Source of induced SA □ Original target shape, no cornealsmoothing (i.e. immediately after ablation) Δ Original target shape, andcorneal smoothing ⋄ Modified target shape (transition zone extended by0.1 mm), no corneal smoothing

As shown here, a target-induced SA (□) may be reduced or even completelyeliminated with a small offset of the transition zone (⋄). In somecases, the offset of the transition zone may cause sharper gradients inthe peripheral target. A 0.05 mm radial shift of the inner boundary ofthe transition zone away from the center of the optical zone, forexample as shown in FIG. 10B, (corresponding to a diameter change of 0.1mm), can make the trend slope for target-induced SA vs. pre-operative SEabout twice as small and bring the magnitude of target-induced SA (⋄)below 0.1 um level, which may be considered negligible. In someinstances, by offsetting the inner boundary of the transition zone (e.g.by about 0.1 mm in diameter), the target induced SA can be reduced byabout 50% (e.g. 0.1 mm change in diameter). As depicted here, correctingthe target induced SA can be effective to remove post-operative SA.

Deconvolution

With returning reference to FIG. 9, a method of modifying a target shapecan also include applying a deconvolution to the target profile orshape, as indicated by step 930. For example, methods may includeapplying a low pass filter (LPF) deconvolution (e.g. with σ=0.35 mm) tothe target profile. Sigma (σ) can refer to a diffusion coefficientrelated to the strength of an LPF process.

According to some embodiments, the application of a deconvolutiontransformation to an original target can operate to compensate for thearea of high curvature, which can be a significant cause ofpost-operatively induced SA.

In some instances, an LPF kernel for a deconvolution may be the same asthe one optimized to fit an observed induced post-operative SA, forexample such as those described above in connection with thepost-operative epithelial smoothing and spherical aberration. Cornealsmoothing, simulated as convolution with an identical or similar LPFkernel, can bring the cornea back to the desired shape.

In some instances, high-frequency variations may be suppressed bydiffusion or LPF convolution. Restoration of such suppressed variationsby deconvolution may introduce inaccuracies, which may also beinfluenced by a signal-to-noise level.

Embodiments of the present invention encompass the use of deconvolutiontechniques which can reduce the degree to which suppressed variationsmay introduce such inaccuracies. For example, deconvolution techniquesmay involve the use of a deconvolution filter, combining an LPF kernel,K, and a signal-to-noise ratio, SNR. The Fourier transform of such afilter can be expressed as follows:

$\begin{matrix}{{{DK}\left( \overset{\rightarrow}{k} \right)} = \frac{K*\left( \overset{\rightarrow}{k} \right)}{{{K\left( \overset{\rightarrow}{k} \right)}}^{2} + {SNR}^{2}}} & {{Equation}\mspace{14mu} 22}\end{matrix}$

Here K(k) represents a Fourier transform of a LPF kernel, the asterisksrefers to a complex conjugate, SNR is the signal-to-noise ratio, and krepresents a vector variable. According to some embodiments, the SNR isassumed to be constant. The value of SNR can define which scales will berestored by the deconvolution, reversing diffusion effect on them. Insome instances, SNR can be 0.1. If the SNR is excessively small, manysmall features may be amplified. If the SNR is excessively large, onlyrelatively large features will be amplified. In exemplary embodiments ofthe present invention, SNR has a value within a range from 0 to 0.1.

If there are no noises and SNR=0, deconvolution should bring backexactly the original target, which existed before the LPF was applied.Where finite noises are present, small features may be irreversibly lostafter low-pass filtering and, therefore, deconvolution may restore theoriginal target only with a finite accuracy. The error of restorationcan be estimated with applying a LPF to a target and then usingdeconvolution to restore it and compare it with the original target.

FIG. 14A shows spherical aberration RMS errors for deconvolution fordifferent SNR values, estimated for study targets (n=340) with σ=0.3 mm,where WFD=6 mm. As depicted here, with SNR=0.1, all SA RMS errors arebelow 0.07 um level. FIG. 14B shows SA errors for a similardeconvolution, estimated for study targets (n=515) with σ=0.28 mm.

Any small and narrow dips in the measured pre-operative wavefront may beamplified by the deconvolution. This may result in small-size featuresthat are too narrow to resolve with laser pulses, which are oftenrestricted to a width of about 1 mm.

In some cases, it is not necessary or desirable to ablate these verynarrow features, as they may be flattened by the smoothing process. Whatis more, these features may also have little influence on the visionquality. In some cases, it is possible to effect the deconvolution so asto neglect or minimize these features and amplify only relativelylarge-scale features of the ablation target. For example, this can bedone by optimizing the SNR value in a deconvolution process. It has beenfound that by using SNR≧0.1, for example, any features smaller than 0.5mm are not amplified by deconvolution. Hence, SNR=0.1 may be used adefault parameter.

A deconvolved target typically has an oscillating profile at theperiphery. These oscillations may be mainly caused by boundaries betweenthe optical zone, transition zone, and an edge of the finite-sizetarget, where either the target profile or its derivatives have sharpchanges.

Embodiments of the present invention encompass the use of deconvolutionand related techniques to compensate for the post-operative induction ofhigh order aberrations (HOAs), and in particular spherical aberration(SA). Accordingly, the visual quality of patients receiving treatmentsaccording to these techniques provides desirable results, particularlyin the management of night vision symptoms. Often, deconvolutionprocedures will result in treatment target shape changes near theperiphery of the optical zone. For example, within a central 4 mm area,the refraction of a modified target shape may be similar or identical tothat of an original target shape.

According to some embodiments, to obtain a new or modified target shape,a deconvolution process can be employed as follows:

$\begin{matrix}{T_{new} = {{K_{INV} \otimes T_{current}} = {{F\left\lbrack \frac{K*\left( {k_{x},k_{y}} \right)}{{{K\left( {k_{x},k_{y}} \right)}}^{2} + {SNR}^{2}} \right\rbrack} \otimes T_{current}}}} & {{Equation}\mspace{14mu} 23}\end{matrix}$

where F(•) stands for a Fourier transform, * denotes a complexconjugate, T_(current) is an original treatment target, T_(new) is thenew target that is intended to remove the post-operative SA, and K_(INV)is the inverse kernel of K. The SNR can be used to prevent or inhibitnoise amplification and oscillation at the edge. In some instances, aSNR value of 0.1 may be suitable for practical purposes. To prevent oras a substitute for real-time calculation of the Fourier transforms, theinverse kernel K_(INV) can be pre-calculated and applied in real-time asa look-up table or a resource file. A suitable SNR value can prevent thedenominator from being zero or excessively small, which may otherwiseresults in the matrix quotient being unreasonably large.

According to some embodiments, an inverse kernel can be exemplified as aconvolution kernel that operates like a deconvolution procedure. In thissense, a deconvolution operation may be considered to be an inverseprocedure of a convolution operation.

Embodiments of the present invention encompass techniques forcalculating an inverse smoothing kernel K_(INV). Whereas a low passfilter (e.g. Butterworth kernel) such as K(x, y) is in the Fourierdomain, the inverse kernel is in the spatial domain. Instead ofimplementing a Fourier transform, it is possible to perform a spatialconvolution implemented as multiplication.

In some cases, embodiments encompass rapid convolution calculations(e.g. in the order of several milliseconds) for UI (user interface)manipulation, in a practical implementation. A normal implementation fora spatial 2-D convolution may involve four netted loops each with 101elements. Such embodiments may be related to the 101×101 mesh size casesdiscussed above in the paragraph following Equation 17. A 2-D spatialconvolution can be written as follows:

$\begin{matrix}{{T_{new}\left( {i,j} \right)} = {{T_{current} \otimes K_{INV}} = {\sum\limits_{k = {- \infty}}^{\infty}\; {\sum\limits_{l = {- \infty}}^{\infty}\; {{T_{current}\left( {{i - k},{j - l}} \right)}{K_{INV}\left( {k,l} \right)}}}}}} & {{Equation}\mspace{14mu} 24}\end{matrix}$

where K_(INV) is the 2-D inverse smoothing kernel. In some cases,K(k_(x), k_(y)) may be a Butterworth of the first kind, and its inversemay have an actual size that is only a few pixels wide. Therefore,Equation 24 may be rewritten as follows:

$\begin{matrix}{{T_{new}\left( {i,j} \right)} = {{T_{current} \otimes K_{INV}} = {\sum\limits_{k = {- s}}^{s}\; {\sum\limits_{l = {- s}}^{s}\; {{T_{current}\left( {{i - k},{j - l}} \right)}{K_{INV}\left( {{51 + k},{51 + l}} \right)}}}}}} & {{Equation}\mspace{14mu} 25}\end{matrix}$

where the inverse kernel size is treated as (2s+1)×(2s+1) in size. Whens=17, or the inverse kernel frame size of 35×35, RMS error usingEquation B is about 0.01 microns. With s=37, use of Equation 25 may beabout 7 times faster than Equation 24, but the error is within 0.001microns. FIG. 23 shows the relationship between the RMS error and thesize of s (pixels), with a simulation of 515 eyes. This figure depictsthe RMS error as a function of s when Equation 25 is used (e.g. incontrast to Equation 28 as discussed below).

Zero Out

With returning reference to FIG. 9, a method of modifying a target shapecan also include zeroing out an ablation profile at distances greaterthan the transition zone radius, as indicated by step 940.

Typically, no ablation is performed beyond the end of transition zone.Hence, it is possible to zero-out the ablation profile at distancesgreater than the transition zone outer radius, R_(TZ), as discussedelsewhere herein, for example with regard to FIGS. 16C and 16D.

A zeroing-out procedure can be included, so as to prevent artifacts andthe like that might occur as a result of performing convolution ordeconvolution. For example convolution or deconvolution mayinadvertently or unintentionally introduce nonzero or negative values atpositions outside of the transition zone. A zeroing-out operation can beinstituted as a safeguard, so as to ensure that such non-zero ornegative values are removed, which could otherwise cause complicationsfor a tissue ablation protocol.

Rescaling Deconvolved Target

As shown in FIG. 9, a method of modifying a target shape can alsoinclude rescaling a deconvolved target, as indicated by step 950. Forexample, a deconvolved target can be rescaled so that its Zernikedefocus term within a 4 mm diameter is the same as that for an originaltarget. In this way, the spherical equivalent refraction of a modifiedor deconvolved target can be the same as that for an original target. Insome instances, a rescaling procedure can be performed to ensure thatthe refractive power for a deconvolved target is the same as that for anoriginal target. In some cases, the refractive power for a deconvolvedtarget is the same as that for an original target and no rescaling stepis performed.

According to some embodiments, an original target shape may performadequately for correcting or treating refraction errors, and hence amodified target shape based on the original target shape may begenerated so that the refraction of the modified target is the same asfor the original target. This can be achieved, for example, by rescalingof the deconvolved target so that its defocus Zernike term within the 4mm area (which defines wavefront-based SE) is the same as for thecurrent target. A rescaling coefficient, which is the ratio of thedefocus terms for the current and de-convolved targets, may be expressedas follows:

$\begin{matrix}{{rescale} = \frac{{SE}_{current}}{{SE}_{{de}\text{-}{conv}}}} & {{Equation}\mspace{14mu} 26}\end{matrix}$

The rescaling coefficient may be close to 1, and distributed as shown inFIGS. 15A and 15B. For example, a rescaling coefficient may have a meanvalue of 1.003, such as that which was found for certain studies. Insuch instances, rescaling may not be needed, in practical terms. In norescaling is performed, then resulting refraction errors may be below0.1 D, for example as shown in FIG. 15A. Hence, it may be possible toneglect or ignore such small values. FIG. 15B shows a distribution of SEre-scaling coefficients and refraction errors without rescaling for thestudies (n=340).

According to some embodiments, deconvolution may also affect thecylinder refraction. A magnitude of this effect is illustrated in FIGS.16A and 16B. Here, it is possible to see a comparison of X, Y componentsof astigmatism for an original target and a deconvolved target(simulated for the studies, n=340). The deconvolved targets showslightly higher astigmatism, as compared with the original targets,although the difference is less than 1%.

According to some embodiments, a current or original target T_(current)yields good matching to low order aberrations, and a scaling can beperformed such that the refractive spherical equivalent over 4 mm of thenew or modified target is the same as that of the current or originaltarget. Exemplary studies have shown that such a scaling factor is aboutunity. Therefore, a scaling factor of 1.0 can be assumed in some cases.

In some embodiments, the rescaling process can incorporate scaling orrescaling techniques disclosed elsewhere herein, such as those describedin FIGS. 22, 24, 41, and 42 and the corresponding specification textdescriptions.

Elevating Ablation Profile

As shown in FIG. 9, a method of modifying a target shape can alsoinclude elevating an ablation profile, as indicated by step 960. Forexample, in order to make all ablation values be non-negative, it ispossible to elevate the entire ablation profile so that the lowest pointon the ablation profile is zero or otherwise non-negative. In this way,the ablation profile can be generated so that it does not have negativeheights.

Damping Periphery Of Transition Zone

As shown in FIG. 9, a method of modifying a target shape can alsoinclude damping a periphery of a transition zone, as indicated by step970. For example, a damping multiplier or multiplication factor may beapplied which suppresses the fluctuations of the periphery of the targetshape. In some embodiments, after certain adjustments are made (e.g.such as the adjustment discussed above), a peripheral part of theablation profile may have a small bump, which may be the result of acut-off at the end of the transition zone. Ablating such a bump mayrequire a sequence of many small laser pulses around the transition zoneperiphery. In some cases, this may cause a substantial reduction ofspeed in the entire ablation process. In some cases, the bump may not beneeded because it lies away from the optical zone and its influence onthe wavefront within the optical zone after smoothing may be verylimited. Embodiments of the present invention encompass the applicationof a damping multiplier to the periphery of the transition zone,starting from the distance R_(b) =R _(TZ)−0.5 mm, as Follows:

$\begin{matrix}{T = {T \cdot \left\{ \begin{matrix}\frac{R_{TZ} - R}{R_{TZ} - R_{b}} & {R > R_{b}} \\1 & {R<=R_{b}}\end{matrix} \right.}} & {{Equation}\mspace{14mu} 27}\end{matrix}$

Such a damping multiplier or factor can be used to eliminate or diminishthe bump.

FIG. 16C shows an X cross-section of modifications of an ablationprofile, and FIG. 16D shows a Y cross-section of modifications of anablation profile. In some embodiments, modifications of an ablationprofile (e.g. high myopia study, case ID=21011 OD) may include targetdeconvolution with σ=0.35 mm, as well as an elevation modification, or acut-off beyond the transition zone.

In some cases, a different wavefront diameter may use or benefit from adifferent diffusion coefficient (e.g. for an LPF model) to matchpost-operative measurements. In some cases, it is possible to use anapproximated value of σ=0.35 mm, which is between optimized values for 6mm and 5.5 mm wavefront diameters, as discussed elsewhere herein. Usinga diffusion coefficient such as this for the target deconvolution, it ispossible to predict or calculate a substantial reduction of induced SAfor both WFD=6 mm and WFD=5 mm and also additional ablation depthrequirement. For example, FIG. 17A depicts a simulated post-operative SAfor a 6 mm wavefront, FIG. 17B depicts a simulated post-operative SA fora 5.5 mm wavefront, and FIG. 17C depicts an extra ablation that maybenefit a deconvolved target. As such, these figures demonstrate theeffect of deconvolution on post-smoothing SA and on additional maximumablation depth.

Because deconvolution may amplify noises, the tail or outer periphery ofthe ablation profile may have some bumps. To remove such bumps, adamping multiplier can be applied as

$\begin{matrix}{T^{\prime} = {T \cdot \left\{ \begin{matrix}{2\left( {R_{TZ} - R} \right)} & {R > R_{b}} \\1 & {R \leq R_{b}}\end{matrix} \right.}} & {{Equation}\mspace{14mu} 28}\end{matrix}$

where T′ is the new target after damping, T is the target after Equation14 and R is a variable in radius. R_(TZ) is the transition zone radius,and the cutoff radius R_(b)=R_(TZ)−0.5 mm. This damping multiplier caneffectively and substantially eliminate the bumps.

Results And Data Analysis

Based on certain codes for treatment target creation, the following twophases of simulation studies were conducted. A first phase involvedoptimizing a one-parameter diffusion coefficient such that it bestexplains the clinically observed 6M post-operative spherical aberrationswith the same surgical parameters as these eyes were treated. A secondphase involved verifying that with the use of an optimized diffusioncoefficient, the expected post-operative spherical aberration issignificantly reduced when a deconvolution algorithm is used.

Optimization of a diffusion coefficient was based on data from variousclinical studies and trials, as well as data from commercial sites. Onlyeyes with pre-operative and 6M (3M for iDesign™ system) post-operativewavefront measurements with at least 6 mm diameter were used. As such,340 eyes were from the study, 169 eyes from the commercial sites, and 39eyes from iDesign™ system based study. Of the 340 eyes from a study, 158were in the low to moderate myopia cohort, 75 in the high myopia cohort,26 from hyperopia cohort, 47 from the monovision cohort (dominant eyesonly), and 34 from the mixed astigmatism cohort.

As explained elsewhere herein, a comparison between a simulated and anobserved post-operative spherical aberration can be performed for agiven diffusion coefficient. An optimization process was chosen suchthat the simulated post-operative spherical aberration has asubstantially identical slope as compared with a pre-operative sphericalequivalent to that of the observed post-operative spherical aberration.

Because of variations of the sample size in different cohorts, the 95%confidence bands are different for different cohort. A small overlaparea can be identified for these 95% confidence bands. The optimizeddiffusion coefficient of 0.35 mm was obtained from the overlap area.

According to some embodiments, deconvolution, which can be used toreduce post-operative spherical aberrations, is a physical-model-backedapproach. It is based on the smoothing effect observed from the clinicaldata. Therefore, not only can it account for the increase of thepost-operative spherical aberration, but it can also account for theinduction of other high order aberrations, such as coma, secondaryastigmatism, and secondary spherical aberration. Furthermore, asdiscussed elsewhere herein, it provides a smaller ablation depth ascompared with other techniques (e.g. larger optical zone, largerkeratometric values) used to target the same level of sphericalaberration reduction.

Many of the target shape modification discussed herein can operate tochange a peripheral area of the target so as to reduce the induction ofSA. It is possible to compare such methods, for example when theirparameters are selected to generate a small slope of SA vs. SE trend, asindicated in Table 4. The parameters in this table were selected for thesimulation to achieve a slope of SA vs. SE trend that is about the sameas the slope from the observed clinical data.

TABLE 4 Modification SA vs.SE <SA> std(SA) max |SA| <extraH> max extraHparameter trend slope um um um um um Current target −0.04 0.16 0.16 0.580.0 0.0 dOZ, mm 0.4 −0.01 −0.01 0.10 0.31 11.02 26.0 dK, D 25 −0.01−0.04 0.11 0.33 9.90 25.9 sigma, mm 0.35 0.01 −0.03 0.09 0.29 7.24 17.9

Table 4 provides a comparison of three methods of target modifications,simulated for data from the studies. Parameters for each modificationmethod were chosen to bring the magnitude of simulated slope ofpost-operative SA vs SE trend line down to 0.01. The simulated averagepost-op SA (<SA>), the worst case SA (max |SM|), the average extraablation depth (<extraH>), and the worst case (max extraH) are alsoshown. Sigma (a) is a diffusion coefficient related to the strength ofan LPF process, described elsewhere herein. As shown in Table 4, adeconvolution method (sigma) can virtually eliminate both the mean SAand the SA vs. SE trend slope. Similarly, a widened optical zone method(dOZ) and a cosine correction adjustment method (dK) can also virtuallyeliminate both the mean SA and the SA vs. SE trend slope. Compared withwidened optical zone and cosine adjustment methods, deconvolutiontechniques often require lower amounts of ablation, and hence canprovide useful solutions where saving or maintaining more tissue isdesired.

FIG. 18A shows an X cross-section of modifications of an ablationprofile, and FIG. 18B shows a Y cross-section of modifications of anablation profile. These modifications of an ablation target aresimulated for a high myopia study (study ID=21011 OD, −7.4D/−1.5D×179°).Simulation was performed for a wider optical zone approach (dOZ=0.4 mm),an adjusted cornea curvature for cosine correction approach (dK=25D),and a deconvolution approach (σ=0.35 mm). When evaluating the expectedpost-operative SA, it may be helpful to consider that simulations mayonly show the changing SA vs SE trend line after the targetmodification. In reality the post-operative SA may deviate from thetrend line due to some other factors which are not accounted for. Thesedeviations can be estimated for the current target as follows:

δSA=SA_(observed) ^((6M))−SA_(stimulated) ^((post-op))  Equation 29

Assuming that the same deviations from the trend line can apply to amodified target, it is possible to add δSA to the simulatedpost-operative SA values of every modified target, which can provide arealistic estimate of post-operative distribution of SA. For example,FIGS. 19A and 19B, depict post-operative SA for observed study data(n=340) and expected post-operative SA for de-convolved targets,simulated with σ=0.35 mm for the same eyes, for a 6 mm wavefront and 5.5mm wavefront, respectively.

In addition to piston differences which may be present between theoriginal and modified targets, there may be other shape differences aswell. According to some embodiments, the following metrics can be usedto compare shape differences:

Δ=(H−max(H))−(H _(current)−max(H _(current)))  Equation 30

where H refers to ablation depth or target height.

As illustrated in FIGS. 20A and 20B, target shapes subsequent tosmoothing for two modification methods, namely widening optical zone(dOZ) and deconvolution (sigma) are almost identical within the 6 mmoptical zone. These figures show the differences (i.e. X and Ycross-sections, respectively) between a modified target and an originaltarget, subsequent to smoothing, simulated for a high myopia case(ID=21011 OD, −7.4D/−1.5D×179°). Simulations were performed for a wideroptical zone (dOZ=0.4 mm), an adjusted corneal curvature for cosinecorrection (dK=25 D), and a deconvolution (σ=0.35 mm).

A cosine adjustment can make a different shape with a substantiallyhigher secondary spherical aberration, as depicted in FIG. 21. In somecases, software or systems may allow both a user-defined optical zoneand a user-defined adjustment of corneal curvature (e.g. defining thecosine correction), and these two adjustments can be used for validationfor a deconvolution technique. In some cases, a wider optical zone, mayprovide a closer approximation than a curvature adjustment. FIG. 21shows a post-operating secondary spherical aberration (WFD=6 mm),simulated for study data (n=340). Simulation was performed for originaltargets and for modified targets with a wider optical zone (dOZ=0.4 mm),an adjusted corneal curvature for cosine correction (dK=25 D), and adeconvolution (σ=0.35 mm).

In sum, the three methods for modification of an ablation target(widening optical zone, adjusting cosine correction, and deconvolution)are capable of eliminating a systematic trend in post-operativelyinduced spherical aberration. As shown here, the ablation profiles forthese modifications can present different depths, and deconvolution canprovide a technique which results in a maximum of tissue retention. Thatis, the amount of ablation associated with deconvolution is smaller thanthat of the other methods. In some instances, widened optical zone anddeconvolution techniques may yield almost identical corneal shapes aftersmoothing. In some cases, a widened optical zone technique (e.g. basedon a user-defined optical zone) may be used as a validation for adeconvolution technique.

Treatment Target Creation

As noted elsewhere herein, a treatment target shape may represent orcorrespond to an intended optical surface that is designed to achieve aparticular refractive correction. FIG. 22 depicts a method 2200 forgenerating a target shape, according to embodiments of the presentinvention. Method 2200 may include obtaining a wavefront correspondingto a pupil plane, as indicated by module 2205. For example, for targetcreation, the input can be a Fourier-based wavefront, which representsthe ocular aberrations on the pupil plane. Typically, a laser ablationis performed on the corneal surface, and hence to obtain the targetshape the ocular aberrations are propagated from the pupil plane to thecorneal surface. Accordingly, methods may include propagating thewavefront, as indicated by step 2210, and obtaining a wavefrontcorresponding to a corneal plane, as indicated by step 2215. Anyphysician adjustments or nomogram adjustments can also be represented onthe corneal surface first before they are combined with the ocularaberrations. Hence, the process of obtaining a wavefront at the cornealplane may also be based on an internal sphere adjustment, as indicatedby step 2220, or on a physician adjustment (e.g. Sph+Cyl), as indicatedby step 2225, or both.

In some instances, parameters such as optical zone size and the ablationzone size, which may be user-defined, can be used to determine theablation or target shape within such zones. Thus, the process ofobtaining a raw or original target shape, as indicated by step 2230, maybe based on a selection or definition of an optical zone, an ablationzone, or both, as indicated by step 2235.

A deconvolution technique can be used to deconvolved the raw or originalshape, so as to obtain a deconvolved shape, as indicated by step 2240.Such a deconvolution can operate to reduce post-operative sphericalaberration. Once the deconvolved shape is obtained, a scaling factor canbe applied, as indicated by step 2245, and a cosine effect modificationthat compensates for the loss of energy due to the curved cornea can beapplied, as indicated by step 2250. In some embodiments, the scalingprocess described in step 2245 can incorporate scaling or rescalingtechniques disclosed elsewhere herein, such as those described in FIGS.9, 24, 41, and 42 and the corresponding specification text descriptions.Hence, the final target shape can be determined based on the deconvolvedshape, as indicated by step 2255, optionally considering a scalingfactor, a cosine effect, or both.

In some instances a nomogram adjustment can be applied, as indicated bystep 2260, when obtaining the final target shape. Following creation ofthe final or modified target shape, as indicated by step 2255, thetarget shape can be transmitted to a treatment table generation engine.

Exemplary Techniques for Target Shape Deconvolution

As explained elsewhere herein, treatment target shapes can lead toinduced aberrations, and deconvolution can be applied to such treatmenttarget shapes so as to reduce or inhibit the induced aberrations.

FIG. 24 depicts aspects of a deconvolution method 2400 for a targetshape, according to embodiments of the present invention. As illustratedhere, method 2400 of deconvolving a target shape may include obtaining amesh size as indicated by step 2405 and obtaining a diffusioncoefficient as indicated by step 2410. Method 2400 may also includeobtaining a complex matrix, in Fourier domain, based on a mesh size anddiffusion coefficient as indicated by step 2415.

Complex Matrix

According to some embodiments, a complex matrix K(k_(x), k_(y)) can beapplied to a treatment target to obtain a wavefront change due tocorneal smoothing. The complex matrix can be considered to represent athree dimensional matrix in a Fourier or frequency domain. In somecases, the complex matrix may be a squared Butterworth low-pass filterof the first order. Other types of low-pass filters may be suitable foruse with embodiments of the present invention. In some cases, a low-passfilter may refer to a function or operation that makes details smootherby suppressing high spatial frequency information.

In some instances, the Fourier domain complex matrix can be expressed asfollows:

$\begin{matrix}{{K\left( {k_{x},k_{y}} \right)} = \frac{1}{1 + \frac{\sigma^{2}\left( {k_{x}^{2} + k_{y}^{2}} \right)}{\left( {0.5\mspace{14mu} {dL}} \right)^{2}}}} & {{Equation}\mspace{14mu} 31}\end{matrix}$

where σ represents a diffusion coefficient, k_(x) and k_(y) representfrequency domain variables, and dL represents a mesh size. Optionally,the diffusion coefficient σ can have a value of 0.35 mm and the meshsize dL can have a value of 0.1 mm. In some instances, the diffusioncoefficient can have a value with a range from about 0.2 to about 0.5(see, e.g. FIG. 12A). In some instances, the diffusion coefficient canhave a value with a range from about 0.33 to about 0.4 (see, e.g. FIG.37).

In some instances, the term Fourier transform as used herein may referto a transform operation. In some instances, the term Fourier transformas used herein may refer to a complex valued function produced by atransform process.

Mesh Size

In an exemplary discrete case, a complex matrix K (k_(x), k_(y)) can bebased on a 101×101 mesh size of dL=0.1 mm. Often, such matrix formats(e.g. 101×101) are used when characterizing treatment planning. In somecases, a mesh size or dL may refer to the spacing or spatial distancebetween two neighboring pixels. In some cases, dL may refer to the pixelresolution in the kernel, which can be 101×101 in pixel frame size or 10mm×10 mm in space. When a discrete Fourier transform is involved, it ispossible to represent the frame in 101×101, although it may no longer be0.1 mm because it is in frequency domain (more like cycles per degree).Hence, dL may involve a 0.1 mm spacing in the spatial domain.

In some instances, selection of a kernel or matrix format may representa balance between accuracy and speed concerns. For example, a largerkernel or matrix format such as 101×101 may provide greater relativeaccuracy and lower relative speed, whereas a smaller kernel or matrixformat such as 25×25 may provide lower relative accuracy and greaterrelative speed.

Diffusion Coefficient

As noted above, a complex matrix can also be based on a diffusioncoefficient σ. Typically, a diffusion coefficient σ has a unit oflength. This parameter can describe the strength of corneal smoothingduring and after a refractive surgical procedure, and as such can beconsidered as a biologically related parameter. The parameter can beused to characterize a single individual, or a group of individuals.Based on the analysis of results from several clinical trials, it hasbeen discovered that a diffusion coefficient σ of 0.35 mm is consistentwith such observed data. In some instances, a diffusion coefficient canhave a value within a range from about 0.2 mm to about 0.5 mm. In someinstances, a diffusion coefficient can have a value of about 0.3 mm.

Because a Fourier domain complex matrix can be based on the mesh size,the diffusion coefficient, or both, it follows that a correspondingspatial domain kernel filter, as discussed elsewhere herein can also bebased on the mesh size, the diffusion coefficient, or both.

According to some embodiments, an LPF can be used to emulate thediffusion of corneal tissue cells. Exemplary techniques may involveestimating or receiving a diffusion coefficient value, and using thatvalue to effect a compensation for a high order aberration beforeadministering a treatment such as a laser vision corrective procedure.By pre-compensating for high order aberrations, it is possible to obtainan outcome with a reduced amount of high order aberrations.

Diffusion coefficients may be evaluated based on simulations. Forexample, a diffusion coefficient σ value can be selected for applicationto clinical data in a deconvolution procedure as described herein, andthe expected outcome (e.g. deconvolved target shape) can be compared tothe actual outcome (e.g. clinical data). The diffusion coefficient canbe adjusted or optimized so as to reduce or minimize variance or astandard deviation in the comparison results. Exemplary adjustment oroptimization techniques are described elsewhere herein, for example inconnection with FIGS. 29 to 32A.

Relatedly, embodiments encompass systems and methods for adjustingrefractive surgery parameters, which may include a diffusioncoefficient, for use in a vision treatment. An exemplary method mayinclude inputting or receiving a refractive case, determining a modeloptical surface shape based on the refractive case and a set ofrefractive surgery system parameters, comparing the refractive case andthe model optical surface shape to determine an aberration induced bythe set of refractive surgery system parameters, adjusting the set ofrefractive surgery system parameters so as to inhibit the inducedaberration, and administering the refractive treatment to a patient. Therefractive treatment can be based on the adjusted set of refractivesurgery system parameters.

Matrix Quotient

As depicted by step 2420, methods may include calculating a matrixquotient, where the dividend includes a conjugate of a Fourier domaincomplex matrix (e.g. K*(k_(x), k_(g)), and the divisor includes the sumof a squared modulus of the Fourier domain complex matrix and a signalto noise ratio value. In some cases, the signal to noise ratio value maybe a squared value. An exemplary matrix quotient can be expressed asfollows:

$\begin{matrix}{\left\lbrack \frac{K*\left( {k_{x},k_{y}} \right)}{{{K\left( {k_{x},k_{y}} \right)}}^{2} + {SNR}^{2}} \right\rbrack,} & {{Equation}\mspace{14mu} 32}\end{matrix}$

In some cases, the denominator or divisor of the matrix quotient can becharacterized at least in part by the expression |K(k_(x), k_(y))|^(n),where n is an integer having a value of 2 or more. In some cases, thedenominator or divisor of the matrix quotient can be characterized atleast in part by the expression [|K(k_(x), k_(y))|^(n)+SNR²] where n isan integer having a value of 2 or more and SNR represents a signal tonoise ratio value. Equation 32 may refer to a filtering process that isin the frequency domain. A complex conjugate may be part of thefiltering process.

Spatial Domain Kernel Filter

As depicted by step 2425, methods may also include obtaining a kernelfilter, in the spatial domain, based on an inverse Fourier transform ofthe matrix quotient. An exemplary kernel filter can be expressed asfollows:

$\begin{matrix}{F\left\lbrack \frac{K*\left( {k_{x},k_{y}} \right)}{{{K\left( {k_{x},k_{y}} \right)}}^{2} + {SNR}^{2}} \right\rbrack} & {{Equation}\mspace{14mu} 33}\end{matrix}$

In some cases, the kernel filter of Equation 33 can be provided as apre-calculated or pre-defined matrix, and can be used or saved as alookup table. As discussed elsewhere herein, this kernel filter can alsobe referred to as an inverse kernel K_(INV). Optionally, this kernelfilter can be referred to as K (x, y). This spatial domain filter orinverse kernel can also be provided as a low pass filter, such as aButterworth or Gaussian filter. Optionally, the spatial domain kernelfilter can present a grid or matrix that reflects how the filtered valueof a pixel depends on neighboring pixel values, and is independent ofthe target shape.

Convolving Raw Target

As depicted by step 2435, methods may include convolving a raw ororiginal target shape with the spatial domain kernel filter. Optionally,methods may include receiving, at an input, an original target profileor shape for the eye of the patient, as indicated by step 2430. As shownhere, the spatial domain kernel filter can be based on an inverseFourier transform of a Fourier domain noise filter, for example, whichmay be based on a conjugate of a Fourier domain complex matrix, on amodulus of a Fourier domain complex matrix, or on a combination thereof.In some instances, a Fourier domain noise filter can be characterized byfraction having a numerator comprising a conjugate of a Fourier domaincomplex matrix and a denominator comprising a modulus of the Fourierdomain complex matrix. Method 2400 indicates that an original targetshape T_(current) (x, y) can be convolved with a spatial domain kernelfilter so as to obtain a deconvolved shape T_(new) (x, y), as indicatedby step 2440. In some instances, the deconvolved shape 2440 emphasizescurvature changes, or corners, sharp edges, sharp transitions, and thelike. In some cases, methods may involve the application of a low passfilter deconvolution to a target profile having a slightly extendedoptical zone. In some instances, parameters of a low pass filter can beoptimized by comparing an LPF model prediction against observed clinicaldata.

According to some embodiments, the systems and methods disclosed hereincan implement dual scale kernel techniques, triple scale kerneltechniques, and other multi-scale kernel techniques (e.g. multipleparameters in a healing kernel), such as those disclosed in U.S.Provisional Patent Application No. 61/871,120 filed Aug. 28, 2013, U.S.patent application Ser. No. 14/453,068 filed Aug. 6, 2014, and U.S.patent application Ser. No. 14/523,467 filed Oct. 24, 2014, the contentof each of which is incorporated herein by reference. According to someembodiments, such kernel scale techniques can be implemented in ahealing kernel, such as that shown in step 2415 of FIG. 24.

Other Refinements

As depicted by step 2445, methods may include additional refinements ofa shape prior to transmitting the shape to a treatment table engine. Forexample, a convolved profile may include a transition zone radius, andexemplary techniques may include zeroing the convolved profile atlocations outside of the transition zone radius. In some cases, anoriginal target profile may have an original refractive sphericalequivalent value within a 4 mm diameter area, and the convolved targetprofile may have a target refractive spherical equivalent value within a4 mm diameter area, and method 2400 may include scaling the originalrefractive spherical equivalent with the target refractive sphericalequivalent value. In some embodiments, the scaling process canincorporate scaling or rescaling techniques disclosed elsewhere herein,such as those described in FIGS. 9, 22, 41, and 42 and the correspondingspecification text descriptions. In some cases, methods may includeelevating the convolved profile so that a lowest point on the convolvedprofile is zero or greater. In some cases, a convolved profile mayinclude a transition zone radius, and methods may involve applying adamping multiplier at or near the transition zone radius. In someinstances, refinement can be performed prior to, or subsequent to,deconvolution, with an equivalent effect.

As discussed elsewhere herein, a deconvolved target may have anoscillating profile at the periphery. Such oscillations may be caused byboundaries between the optical zone, transition zone, and edge of thefinite-size target, where either the target profile or its derivativeshave sharp changes. In some instances, it may be helpful to elevate theentire ablation profile so that the lowest point on the ablation profileis zero, or so that all ablation values are non-negative. What is more,it may be helpful to zero-out the ablation profile at distances greaterthan the transition zone radius, R_(TZ), where no ablation is desiredbeyond the end of the transition zone. Such refinements are illustratedin the X and Y target cross-sections of FIG. 25A, which depictsmodifications of an ablation profile (high myopia study, case ID=21011OD) including deconvolution (σ=0.28 mm), elevation, and cut-off beyondthe transition zone. In some cases, after such refinements oradjustments are made, only the peripheral curvature will be changed, forexample as depicted in FIG. 25B, which shows a change of ablationprofile after target deconvolution (High Myopia study, case ID=21011,OD, −7.4D/−1.5D×179 deg).

In some instances, an original target shape may operate to effectivelyaddress refraction errors, and hence it may be desirable to maintain therefraction of the modified target at the same value as the refraction ofthe original target. This can be done with rescaling of the deconvolvedtarget so that its defocusing term within the 4 mm area is the same asfor the original target. In some embodiments, the rescaling process canincorporate scaling or rescaling techniques disclosed elsewhere herein,such as those described in FIGS. 9, 22, 24, 41, and 42 and thecorresponding specification text descriptions.

In addition to, or following some or all of the above mentionedadjustments, the peripheral part of the ablation profile may have asmall bump, which results mainly from the cut-off at the end of thetransition zone, for example as depicted in FIG. 25A. Ablating such abump may involve application of a sequence of many small laser pulsesaround the transition zone periphery. In some instances, this may leadto a substantial slow-down of the entire ablation process. Yet this bumpmay be unnecessary, because it lies away from the optical zone and itsinfluence on the wavefront within the optical zone shall be rather smallafter healing. With this consideration, it is possible to apply adamping multiplier to the periphery of the transition zone, as describedelsewhere herein.

Spherical Aberration and Related Topics

As discussed elsewhere herein, spherical aberration (SA) may be inducedby a target shape, a healing effect, or a combination thereof. In somecases, it is possible to reduce or even completely eliminatetarget-induced SA by implementing a small offset of the transition zone.In some original target shapes, the inner boundary of the transitionzone is located within the optical zone, e.g. at about 0.25 mm from theedge of the optical zone. In addressing target-induced SA, it may behelpful to shift the transition zone boundary, by moving it farther fromthe center of the optical zone. In this way, the target-induced SA canbe decreased, although squeeze the transition zone and cause sharpergradients in the peripheral target. In some instances, this may meanthere will be a narrower transition zone band. In some instances,shifting the inner boundary of the transition zone away from the centerof the optical zone by a distance of about 0.1 mm can operate to reducethe target-induced SA to a level below 0.1 um, which may be considerednegligible.

FIG. 26 shows a simulated induced SA immediately after ablation(target-induced) and after healing (total) for a target with an innerboundary of the transition zone shifted outward by 0.1 mm, using ahealing model where σ=0.28 mm. As shown here, after healing, the totalSA reached a level of about 0.3 um.

In order to compensate for the spread of the high curvature, which is amain cause of post-healing induced SA, it is helpful to apply adeconvolution transformation to the original target. In some cases, theLPF core for deconvolution is the same as the one optimized to fitobserved induced post-operative SA. Then healing, simulated asconvolution with the same LPF core, can bring the healed cornea back tothe desired shape.

FIG. 27 shows the effect of deconvolution on post-healing SA (leftpanel) and additional maximum ablation depth (right panel) simulatedwith σ=0.28 mm for studies (n=515). Relatedly, Table 5 shows simulatedchanges in post-healing SA and extra ablation, caused by deconvolutionand additional adjustments of an original target. Statistics forstudies: Myopia and High Myopia (n=327), Hyperopia (n=43), and allstudies together (n=515).

TABLE 5 old SA(SE) new SA(SE) Slope Slope <SA> max |SA| <extra Abl> maxextAb Myopia & HM −0 04 −0.01 0.01 0.08 4.3 8.9 Hyperopia −0.05 −0.02−0.05 0.11 3.5 7.6 All US IDE −0.04 −0.01 0.00 0.11 4.2 9.9

FIG. 28 depicts a radial compensation function (RCF) for a deconvolvedtarget in a high myopia case, according to embodiments of the presentinvention. Specifically, a radial compensation function was calculatedfor a deconvolved target corresponding to a High Myopia study (caseID=21011 OD, −7.4D/−1.5D×179 deg.). As shown here, the RCF is almostflat in the central part and decreases in the periphery.

FIG. 29 schematically illustrates techniques for obtaining andimplementing a modified target shape, according to embodiments of thepresent invention. As shown here, study data can be used to deriveparameters of a kernel for simulating a low-pass filtering process, forcorneal healing and the like. Embodiments may also include optimizingthe parameters by using a clinical data set. These techniques may alsoinvolve evaluating the extent to which observed spherical aberration isattributed to error, due to an imperfect optical treatment shape. Insome instances, methods may also include addressing target shape inducedSA by providing transition zone adjustments, optical zone extensionadjustments, or both. In some cases, a deconvolution (e.g. inverse oflow pass filter) may boost the total treatment depth. Techniques mayalso involve running a revised target controller (e.g. without a cosineeffect) with a low-pass filter, to evaluate the extent to which SA for aclinical data set correlates with observed SA, or to evaluate the extentto which post-operative refractions correlate with what is expectedbased on the clinical data. The Optimized Kernel Parameter can berelated to LPF, and sigma can represent the diffusion coefficient.Hence, as shown in FIG. 29, with a clinical data set 2910, a kerneloptimization process 2912 can be employed such that simulation can beperformed to obtain the optimized kernel parameter (sigma) 2914.According to some embodiment, the value of sigma=0.35 was found tocorrespond to an optimized kernel parameter. For a practicalimplementation, the clinical data 2910 can be sent to a research versionof Target Controller 2918 (in matlab), which is identical to theproduction Target Controller 2926 (in C++). It can be derived from theTarget Controller 2918 that induction of spherical aberration (SA) 2920occurs in the target so a removal of a target-induced SA can beimplemented in a revised Target Controller 2922. The revised TargetController 2922 can implement a new optical zone (OZ) extensionalgorithm 2928, and a new Transition Zone algorithm 2930. With all therevisions, the Revised Target Controller 2922 can be tested with dataset 2924, which can be the same as (or different from) data set 2910.The Revised Target Controller 2922 can then be verified with SA and MRSE(manifest refraction in spherical equivalent) in 2932.

Shape Induced SA

FIG. 30 shows a total induced SA (left panel, 0.188±0.139 for myopia and−0.110±0.179 for hyperopia) and a shape-induced SA (right panel,0.064±0.049 for myopia and −0.071±0.038 for hyperopia) after taking intoaccount a low-pass filtering effect, according to embodiments of thepresent invention. When considering the mean, it is possible to observethat shape-induced SA consists of ⅓ of the total SA for myopia and morethan ½ for hyperopia. When considering the trend line slope, it ispossible to observe that shape-induced SA consists of more than ½ formyopia and less than ¼ for hyperopia. Therefore, a shape-induced SA canbe a significant component for an observed post-surgery sphericalaberration. For the data presented in FIG. 30, the healing effect forthe shape-induced SA was included in the simulation.

Low Pass Filter

Assuming that a particular theoretical target shape provides a best fitfor low order correction it is possible to perform an optimization asfollows. First, an ablation target for an eye (e.g. an eye from a study)can be calculated according to a respective scaling factor and sphereadjustment. Second, a low pass filter (e.g. Butterworth or Gaussian) canbe applied to obtain a healed shape. Third, a residual shape can beobtained by subtracting the healed shape from a pre-operative CV(CustomVue®) treatment shape. Fourth, a residual error in SA (e.g.predicted SA) can be calculated. Fifth, a merit function can becalculated. For example, the merit function may be the square root ofthe average sum of the square difference between the observed SA and thepredicted SA. FIG. 31 shows aspects of optimization of a low passfilter, according to embodiments of the present invention. FIGS. 32A and32B show aspects of a kernel and an inverse kernel, according toembodiments of the present invention.

Shape Deconvolution and Verification

According to some embodiments, it is possible to process a target shapeas follows. First, a theoretical target is created, optionally using azone-extended target algorithm. The target shape is then convolved withan inverse kernel. The convolved shape is them lifted to avoid negativeablation. A scaling factor can then be applied to preserved SE over a 4mm zone. Subsequently, a cosine effect can be applied. FIG. 33 depictsaspects of a treatment target deconvolution according to embodiments ofthe present invention.

According to some embodiments, it is possible to verify such targetshape procedures as follows. First, obtain a theoretical target shapefor an eye (e.g. each eye from a study set). Second, obtain adeconvolved target by convolving the target shape with an inversekernel. Third, convolve the target with a determined kernel (e.g. healedtarget). Fourth, calculate the difference between the theoretical targetand the simulated healed target (e.g. healed target subtracted fromtheoretical target). FIG. 34 depicts aspects of a target verificationprocedure according to embodiments of the present invention. FIGS. 35A,35B, and 35C depict residual error with deconvolution, according toembodiments of the present invention.

FIG. 36 depicts expected targets (left column), inversed convolvedtargets (middle column), and the difference between expected andinversed convolved targets (right column), according to embodiments ofthe present invention.

Optimization of Kernel

FIG. 37 depicts CV data from a study (515 eyes, including myopia,hyperopia, high myopia, and mixed cases, as well as VSS-R™ treatmentdata from a Canadian study (77 eyes, including myopia [mostly], and afew hyperopia and mixed cases). FIG. 37 indicates that the optimizedsigma for various data sets suggests a range between about 0.33 mm andabout 0.40 mm.

Post-Operative SA (Expected vs. Actual)

FIG. 38 depicts actual vs. expected post-operative sphericalaberrations.

Other Features

FIG. 39 depicts cylinder like cases (top row), mixed cases (middle row),and hyperopia cases (bottom row), according to embodiments of thepresent invention.

Treatment Validation

Embodiments of the present invention encompass systems and methods fortreatment validation based on low order aberrations. In some cases,embodiments of the present invention encompass systems and methods fortreatment validation based on sphere-cylinder coupling. In some cases,embodiments of the present invention encompass systems and methods fortreatment validation based on high order aberrations.

As discussed elsewhere herein, various deconvolution techniques can beimplemented so as to remove or reduce LASIK-induced sphericalaberration. Embodiments of the present invention encompass treatmentvalidation systems and methods to ensure that treatments can provide adesired clinical outcome. For example, validation techniques can beimplemented to ensure that low order and high order aberrationsassociated with a developed treatment are consistent with the desiredproduction target shape features. Various verification techniques aredisclosed, including approaches related to the preservation of low orderaberrations, approaches involving cylinder coupling, and approachesrelated to the addition of spherical aberration with the use ofdeconvolution.

Treatment Validation (Low Order Aberrations)

Various clinical studies have been performed, for example to treat lowto moderate myopia, high myopia, hyperopia, mixed astigmatism, andmonovision, using wavefront guided treatments. In some cases, desiredclinical outcomes were achieved using basis data and related adjustmenttechniques, such as those described in U.S. Provisional PatentApplication Nos. 61/724,111 and 61/765,567 filed Nov. 8, 2012 and Feb.15, 2013, respectively, as well as those described in [KT 91288-868098(043800US)], the contents of each of which are incorporated herein byreference. In some cases, desired clinical outcomes were achieved usinginternal sphere adjustment techniques.

The graph in FIG. 40 illustrates attempted (or intended) MRSE versusachieved MRSE (Manifest Refraction Spherical Equivalent) for eyes inseveral clinical trials. As depicted here, there is a good match betweenthe achieved MRSE and the attempted MRSE, with little deviation.

According to some embodiments, the attempted MRSE can refer to a target,and the achieved MRSE can refer to a clinical outcome. In some cases,the attempted MRSE can be considered to be analogous or equivalent tothe raw target shape of step 2230 in FIG. 22. In some cases, theattempted MRSE can be considered to be analogous or equivalent to theexisting target 4110 in FIG. 41.

According to some embodiments, the term attempted MRSE can be usedinterchangeably with the term intended MRSE. In some cases, the termexpected MRSE can refer to an expected post-operative MRSE or anexpected achieved MRSE. The term expected achieved MRSE can refer to apre-operative MRSE minus a post-operative MRSE.

FIG. 41 depicts aspects of a target development process, according toembodiments of the present invention. As shown here, the process mayinvolve SE scaling for a deconvolved treatment target. Exemplarytechniques may involve obtaining an existing target 4110, anddeconvolving the target 4110 with a low pass filter 4120 to obtain adeconvolved target 4130. In some cases, a low pass filter can bereferred to as an optimized linear filter. Hence, a low pass filter (oroptimized linear filter) can be applied to the existing target to obtainthe deconvolved target. Refraction measures, such as wavefront sphericalequivalents, can be obtained. For example, a refraction measure 4140(e.g. 4 mm refraction or 4 mm WRSE) of the existing target 4110 can beobtained, and a refraction measure 4150 (e.g. 4 mm refraction or 4 mmWRSE) of the deconvolved target 4130 can be obtained. The term MRSE canrefer to manifest refraction spherical equivalent, and the term WRSE canrefer to wavefront refraction spherical equivalent. The terms MRSE andWRSE are similar in that they both refer to measurements of refraction.According to some embodiments, the existing target 4110 depicted here isanalogous or equivalent to the T_(current) discussed elsewhere herein(e.g. depicted in FIG. 24). According to some embodiments, the existingtarget 4110 depicted here is analogous or equivalent to the raw ororiginal target shape discussed elsewhere herein (e.g. depicted in FIG.22).

A scale factor or ratio 4160 can be obtained based on the existingtarget refraction measure 4140 and the deconvolved target refractionmeasure 4150. For example, a factor can be determined based on the ratioof the 4-mm WRSE of the existing target to the 4-mm WRSE of thedeconvolved target. As shown here, techniques may also involve applyingthe scale factor 410 to the deconvolved target 4130 to obtain a scaletarget 4170. A final target 4180 can be obtained based on the scaletarget 4170.

According to some embodiments, a desired objective may involve having anexisting target refraction measure 4140 that matches or approximates thedeconvolved target refraction measure 4150. For example, preservation ofthe refractive power of the target following convolution can provide anindication of a good clinical outcome.

The relationship between attempted MRSE and achieved MRSE shown in FIG.40 is based on actual data analysis of clinical observations. It ispossible to perform modeling using an intended (or attempted) MRSE (orWRSE) versus an expected MRSE (or WRSE). The scaling techniquesdiscussed herein, for example in FIGS. 9, 22, 24, 41, and 42, can beimplemented to achieve an “attempted” versus “achieved MRSE (or WRSE)correlation, for example with a unity slope. Relatedly, with regard toFIG. 41, the measured refraction 4140 can be analogous to the attemptedrefraction, and the measured refraction 4150 can be analogous to theachieved refraction. In this sense, a process of ensuring that theoutcome is good (e.g. a good match between refraction measures 4140 and4150) can be referred to as validation. For example, as the treatmenttarget shape is changed by deconvolution, steps can be taken to ensurethat the refraction measure (e.g. 4 mm WRSE) of the new deconvolvedtarget is the same as or approximates the refraction measure (e.g. 4 mmWRSE) of the existing target. Hence, the objective of obtaining a goodclinical outcome, in terms of low order aberrations, can be achieved.Techniques for obtaining a good clinical outcome in terms of high orderaberrations are discussed elsewhere herein.

According to some embodiments, validation may involve determining atreatment target based on a treatment table, comparing the treatmenttarget to a wavefront refraction, and evaluating whether the comparisonis within a certain tolerance.

According to some embodiments, the low pass filter 4120 or deconvolutiontechnique can be validated, based on whether there is a good orsufficient match between the existing target refraction measure 4140 andthe deconvolved target refraction measure 4150. For example, low orderaberrations of the existing target are sufficiently close to low orderaberrations of the deconvolved target, then the low pass filter can beconsidered to exhibit the desired performance.

According to some embodiments, the low pass filter 4120 can provide anapproximation or simulation of how a laser will deliver a treatment.Hence, by constructing an optical surface and calculating thecorresponding refraction, it is possible to compare the refraction to anintended refraction, to validate the low pass filter.

As explained elsewhere herein, a target (or a deconvolved target) can beprocessed using simulated annealing techniques or other methods toobtain a sequence of laser instructions for a patient eye treatment.According to some embodiments, if the difference between the existingtarget refraction measure 4140 and the deconvolved target refractionmeasure 4150 exceeds a certain threshold or amount, then a decision maybe made to not proceed with administration of the treatment to thepatient.

For a given low pass filter (LPF), a scaling factor can be determinedfor each eye. Various techniques can be used to determine a scalingfactor. For example, as depicted in FIG. 42, a scaling factor can bedetermined (1) using a population mean, (2) using individual scalingbased on the target refraction, or (3) using individual scaling based on“healed” target refraction. The scaling methods depicted here encompasstechniques for low order refraction scaling.

The term T0 can refer to the original or existing treatment target. Theterm TC can refer to a Target Controller, which may include a softwareand/or hardware module that generates the original or existing treatmenttarget. The term T1 can refer to a deconvolved target. The term T2 canrefer to a scaled target of T1.

As depicted in version (1) here, an exemplary method of determining avision treatment for an eye of a patient can include receiving, at aninput, an original target T0 or target profile for the eye of thepatient. The existing target can be obtained from or generated by atarget controller, as shown in step 4202. Exemplary methods may alsoinclude obtaining a deconvolved target T1 or target profile based on theoriginal target profile and a low pass filter. For example, target T1can be determined by deconvolving target T0 with a low pass filter (oroptimized linear filter). As shown at step 4204, T1 can be processedwith an inverse kernel K_(INV). As discussed elsewhere herein, aninverse kernel can be exemplified as a convolution kernel that operateslike a deconvolution procedure. In this sense, a deconvolution operationmay be considered to be a convolution procedure using an inverse kernel.Step 4206 indicates that a deconvolved target T1 can be obtained via adeconvolution process. Further, exemplary methods may include obtaininga scale factor, where the scale factor is based on a low orderrefraction measure of a test eye population and a low order refractionmeasure of a convolved test eye population profile, and where theconvolved test eye population profile is based on a convolution of thetest eye population profile. In some cases, the scale factor is aconstant. As shown here in step 4208, the scale factor can be 0.599. Insome embodiments, the scale factor can be 0.7489. According to someembodiments, the scale factor can have a value within the range fromabout 0.4 to about 0.8. As indicated in step 4210, methods may includedetermining a scaled target T2 or target profile based on thedeconvolved target T1 or target profile and the scale factor. Exemplarymethods may also include determining the vision treatment based on thescaled target T2 or target profile.

As noted above, a scale factor can be based on a low order refractionmeasure of a test eye population and a low order refraction measure of aconvolved test eye population profile. In some cases, the low orderrefraction measure of the test eye population profile includes a firstmanifest refraction spherical equivalent measure and the low orderrefraction measure of the convolved test eye population profile includesa second manifest refraction spherical equivalent measure. In somecases, the first manifest refraction spherical equivalent measure is a 4mm refraction measure and the second manifest refraction sphericalequivalent measure is a 4 mm refraction measure.

In addition to the population mean scaling factor approach depicted inversion (1), embodiments of the present invention also encompass otherlow order refraction scaling approaches, such as individual scalingtechniques that involve scaling factors based on targets. As depicted inversion (2) here, an exemplary method of determining a vision treatmentfor an eye of a patient can include receiving, at an input, an originaltarget profile T0 for the eye of the patient. The existing target T0 canbe obtained from or generated by a target controller, as shown in step4222. Methods may also include determining a first low order refractionmeasure, for example SE (T0), based on the original target profile T0,as indicated by step 4224. Further, methods may include obtaining adeconvolved target profile based on the original target profile and alow pass filter. For example, target T1 can be determined bydeconvolving target T0 with a low pass filter (or optimized linearfilter). As shown at step 4226, T1 can be processed with an inversekernel K_(INV). Step 4227 indicates that a deconvolved target T1 can beobtained via a deconvolution process. Methods may also includedetermining a second low order refraction measure based on thedeconvolved target profile. For example, a second low order refractionmeasure, such as SE (T1), can be determined based on the deconvolvedtarget profile T1, as indicated by step 4228. According to theembodiment depicted in version (2), methods may also include determininga scale factor based on a comparison between the first and second loworder refraction measures. For example, a scale factor α can bedetermined based on a comparison between first low order refractionmeasure SE (T0) and second low order refraction measure SE (T1). Asshown here in step 4230, the scale factor α can include a ratio of thefirst low order refraction measure SE (T0) and the second low orderrefraction measure SE (T1). Further, methods may include determining ascaled target profile based on the deconvolved target profile and thescale factor. For example, as depicted in step 4232, methods may includedetermining a scaled target profile T2 based on a deconvolved targetprofile T1 and a scale factor α. Methods may also include determiningthe vision treatment based on the scaled target profile.

As depicted here, the first low order refraction measure can include afirst manifest refraction spherical equivalent (SE) measure. Relatedly,the second low order refraction measure can include a second manifestrefraction spherical equivalent (SE) measure. In some instances, thefirst low order refraction measure (e.g. first manifest refractionspherical equivalent measure) is a 4 mm refraction measure. In someinstances, the second low order refraction measure (e.g. second manifestrefraction spherical equivalent measure) is a 4 mm refraction measure.In some instances, the first low order refraction measure includes afirst sphere measure. In some instances, the second low order refractionmeasure includes a second sphere measure. In some instances, the firstlow order refraction measure includes a first cylinder measure. In someinstances, the second low order refraction measure includes a secondcylinder measure.

Hence, the embodiment depicted by version (2) in FIG. 42 encompassestechniques where T1 represents a target T0 as convolved with an inversekernel. The ratio α may be different for different eyes. Hence, incomparison to the population approach of version (1), this version canbe used for an individualized or customized approach. The ratio α can bedetermined for individual persons, on a per eye basis.

In addition to the population mean scaling factor approach depicted inversion (1), and the individual scaling technique depicted in version(2), embodiments of the present invention also encompass other low orderrefraction scaling approaches, such as individual scaling techniquesthat involve scaling factors based on healed target refractions. Asdepicted in version (3) here, an exemplary method of determining avision treatment for an eye of a patient can include receiving, at aninput, an original target profile T0 for the eye of the patient.

According to some embodiment, T0 can refer to the target (e.g.corresponding to tissue ablation depth over a 101×101 space). TC canrefer to a target controller, and may include a software and/or hardwaremodule that generates the treatment target. T1 can refer to adeconvolved target. T2 can refer to a scaled target of T1. T4 can referto a convolved target (e.g. simulating the healed target of T0). T6 canrefer to a healed target of T1 (e.g. the deconvolved target healed).

The existing target T0 can be obtained from or generated by a targetcontroller, as shown in step 4242. Methods may also include obtaining afirst healed profile based on the original target profile. For example,a first healed profile T4 can be determined based on an original targetprofile T0 as indicated by step 4246. The healing can be represented bya healing kernel K. When a target is convolved with K, the targetbecomes a healed target (i.e. simulating the healing process). Adeconvolution is a reverse process of convolution. Further, adeconvolution can be treated as a convolution process, by obtaining aninverse kernel invK. For example, if the healed target is convolved withinvK, it is possible to obtain the original target T0. Put another way,if A*K=B, it is possible to have B*invK=A, where * stands forconvolution and invK is the inverse kernel of K. Accordingly, Target T4can be determined based on original target (e.g. T0) and convolutionwith kernel K. As such, T4 can be considered a healed case for T0, wherethe healed outcome is considered to be approximated by the convolution.Further, methods may include obtaining a deconvolved target profilebased on the original target profile and a low pass filter. For example,target T1 can be determined by deconvolving target T0 with a low passfilter (or optimized linear filter). As shown at step 4248, T1 can beprocessed with an inverse kernel K_(INV). Step 4250 indicates that adeconvolved target T1 can be obtained via a deconvolution process.Exemplary methods may also include obtaining a second healed profilebased on the deconvolved target profile, as indicated by step 4254. Forexample, a second healed profile T6 can be determined based on thedeconvolved target profile T1. Accordingly, based on the discussionabove, Target T6 can be determined based on a target (e.g. T1) andconvolution with kernel K. As such, T6 can be considered a healed casefor T1, where the healed outcome is considered to be approximated by theconvolution.

As shown here, methods may include determining a first low orderrefraction measure, such as SE (T5), based on the first healed profileT5, and a second low order refraction measure, such as SE (T6), based onthe second healed profile T6. As shown in step 4256, methods may includedetermining a scale factor α based on a comparison (e.g. a ratio)between the first low order refraction measure and the second low orderrefraction measure. Further, methods may include determining a scaledtarget profile based on the deconvolved target profile and the scalefactor. For example, as depicted in step 4258, methods may includedetermining a scaled target profile T2 based on a deconvolved targetprofile T1 and a scale factor α. Methods may also include determiningthe vision treatment based on the scaled target profile.

In some cases, the first low order refraction measure can include afirst manifest refraction spherical equivalent measure. In some cases,the second low order refraction measure can include a second manifestrefraction spherical equivalent measure. In some cases, the firstmanifest refraction spherical equivalent measure can include a 4 mmrefraction measure. In some cases, the second manifest refractionspherical equivalent measure can include a 4 mm refraction measure. Insome cases, the first low order refraction measure can include a firstsphere measure. In some cases, the second low order refraction measurecan include a second sphere measure. In some cases, the first low orderrefraction measure can include a first cylinder measure. In some cases,the second low order refraction measure can include a second cylindermeasure.

Hence, according to version (1) depicted in FIG. 42, a number of testeyes (e.g. eyes from previously performed clinical trials) can be used.Treatment targets can be determined and their associated 4-mm WRSEvalues can be calculated. What is more, respective deconvolved targetsfor the same eyes can be determined and their associated 4-mm WRSEvalues can be calculated. For each eye, a ratio of the existing targetWRSE over the deconvolved target WRSE can be calculated. A mean valuecan be calculated such that it can be used to be implemented in thedeconvolved target to scale the target before it is finally generated.With the implemented scaling, those same eyes can be used to verify thatthe WRSE for the deconvolved scaled targets is the same as the WRSE forthe existing target over a 4-mm pupil. FIG. 43 provides results for awavefront based LASIK (e.g. using WaveScan®, CustomVue®) in the upperpanel and a refraction based LASIK (e.g. using VSS Refractive™) in thelower panel, where a scaled deconvolved target SE is compared with anexisting target SE. As shown here, the results confirm that a constantscaling factor approach such as that described in version (1) of FIG. 42(e.g. using a scaling factor of 0.599) can provide a good match for thedeconvolved scaled target versus the existing target. To the extent thatthe terms MRSE and WRSE are interchangeably used, it is understood thatboth terms refer to types of spherical equivalent (SE), and hence theusage refers to that common aspect, while acknowledging the differencebetween the wavefront nature of WRSE and the manifest nature of MRSE.Accordingly, there the terms WRSE and/or MRSE are used, it is alsopossible to replace those terms with the more generic term SE.

As noted above with regard to version (2), a scaling technique can bebased on an individualized approach, in contrast to the fixed constantapproach provided in version (1). According to some embodiments, whenusing version (2), when the deconvolved target has a very low SE (e.g.which may occur in cases with mixed astigmatism), any noise can beamplified. In such instances, a different formula, such as sphere orcylinder can be used instead.

As noted above, version (3) also pertains to a scaling technique that isbased on an individualized approach. According to version (3), thecalculation can be performed using a “healed” target determination.

To confirm the outcome, in particular for myopia, 327 myopic eyes wereused for simulation. Use of a scaling factor shows that the deconvolvedtarget is expected to have the same 4-mm refraction as the originaltreatment target. The three versions (1), (2), and (3) of FIG. 42 depictthree ways of obtaining a reasonable scaling factor. An LPF kernel wasused to simulate the low pass filtering or “healing” process. When atreatment target is convolved with the kernel, a post-operative shape(e.g. convolved or healed shape) can be determined. FIG. 44 shows the4-mm refraction for the intended versus achieved from the treatmenttarget, for both the current (upper left panel) and the deconvolved(upper right panel) targets. In the lower panels, the 4-mm refractionfrom the simulated post-operative shapes are used to compare to thepre-operative wavefront refraction, again for both the current (lowerleft panel) and the deconvolved (lower right panel) targets. Because thedeconvolved target has the same regression slope as the current targetfrom both the target view point and from the “healed” target, it can beconcluded that a significant amount of low order aberration ispreserved.

According to some embodiments, the scaling technique disclosed thereincan help to ensure that the post-operative patient does not exhibit anundue amount of sphere and cylinder. In some cases, reduction of sphere,cylinder, or both can be enhanced using a nomogram adjustment. Nomogramadjustments can be implemented in manual or automated processes. In somecases, the convolution (or healing) techniques disclosed herein canexplain the effects of epithelial remodeling. In some case, as furtherdiscussed herein, the convolution techniques can be used to explaineffects associated with the sphere and cylinder coupling.

Sphere-Cylinder Coupling

As depicted in FIG. 40, the techniques disclosed herein can produce nearoptimal clinical outcomes (e.g. a good match between the achieved MRSEand the attempted MRSE). In some instances, target developmenttechniques may produce an amount of under-correction in cylinder. Insome instances, target development techniques (e.g. using a low passfilter) may produce an amount of sphere-cylinder coupling. For example,the pre-operative cylinder may affect the post-operative sphere,although the spherical equivalent value is maintained. A higher cylinderin minus notation pre-operatively may cause a higher shift in thehyperopic direction in sphere post-operatively. This can be observed inFIG. 105, when the sphere and cylinder are measured in manifest andwavefront refractions. Cross-coupling phenomenon can be measured aspost-operative sphere as a function of the pre-operative cylinder formanifest (upper panel) and wavefront (lower panel).

To help ensure that both the sphere and cylinder are close to zeropost-operatively, a nomogram is proposed to be used by the physicians toenter into the “Physician Adjustment” for the sphere correction based onthe pre-operative wavefront cylinder. According to some embodiments,this Physician Adjustment can be used at module 2225 in FIG. 22. Thenomogram provided in Table 6 (using absolute value of negative cylinder)can be used:

TABLE 6 Pre-Operative Wavefront Cylinder Physician Adjustment in Sphere(diopters) (diopters) 0.00 to 0.25 −0.25 0.26 to 0.75 −0.13 0.76 to 1.000.00 1.01 to 2.00 0.20 2.01 to 3.00 0.40 3.01 to 4.00 0.60 4.01 to 5.000.80 5.01 to 6.00 1.00 6.01 to 7.00 1.20 7.01 to 8.00 1.40

According to some embodiments, a formula such as S=−0.2C−0.25 can beused, where S represents a sphere adjustment, and C represents apre-operative wavefront cylinder in minus notation, both in diopters.

According to some embodiments, it is possible to observe and/or predictcylinder coupling results. FIG. 46 depicts low order results, where WRSrepresents sphere, and WRC represents cylinder. To assess effects due toa low pass filter, a set of patient eyes were used. The targets weresmoothed with an LPF using a 2D convolution and the predictedpost-operative outcome was calculated. Based on FIG. 46, it can be seenthat about 25% of the cylinder coupling may be explained due to thesmoothing. When the deconvolution is implemented, about 33% of thecylinder coupling may be explained. The difference between the two isonly 2.8%, which is well too small compared to the 34% coupling from theobservation (in terms of wavefront refraction, only about 22% in termsof manifest refraction).

These numbers (25%, 33%, 2.8%, 34%, and 22%) can relate to the slopes inthe graph. For example, the slope for an original (or current) targetcan be about 8% (0.0779) which is about 25% of the observed coupling ofabout 34% (0.3389). The difference of slopes between the current and thedeconvolved target is about 2.8% (0.1059−0.0779). The 22% value is alsofrom the slope, but from a different graph (not shown here), and isrelated to the formula (S=−0.2C−0.25). The 22% value can be approximatedwith 0.20. Therefore, it may be desirable to use no additionaladjustment to the nomogram for cylinder coupling. Hence, the formulamentioned above, S=−0.2C−0.25 can be used.

Embodiments of the present invention encompass systems and methods fordetermining a vision treatment which involve adjusting a sphereparameter of a treatment based on a pre-operative cylinder measurement.For example, as shown in FIG. 46A, an exemplary method 4600 may includereceiving, at an input, an original target profile for the eye of thepatient, as indicated by step 4610. Methods may also include obtaining adeconvolved target profile based on the original target profile and alow pass filter, as indicated by step 4620. Further, methods may includeobtaining a scale factor, as indicated by step 4630. The scale factorcan be based on a low order refraction measure of a test eye populationand a low order refraction measure of a convolved test eye populationprofile. The convolved test eye population profile can be based on aconvolution of the test eye population profile. Methods may also includedetermining a scaled target profile based on the deconvolved targetprofile and the scale factor, as indicated by step 4640. Further,methods may include adjusting a sphere parameter of the scaled targetprofile based on a pre-operative cylinder measurement 4650 of the eye ofthe patient, as indicated by step 4660. In some cases, methods may alsoinclude determining the vision treatment based on the adjusted targetprofile, as indicated by step 4670. According to some embodiments,methods for determining a vision treatment for an eye of a patient mayinclude obtaining a pre-operative cylinder value for the eye of thepatient, for example by receiving, at an input, a pre-operative cylindervalue for the eye of the patient, and determining the vision treatmentfor the eye, where the vision treatment includes a sphere value that isbased on the pre-operative cylinder value. In some cases, apre-operative cylinder value can correspond to a manifest refractionmeasurement. In some cases, a pre-operative cylinder value cancorrespond to a wavefront refraction measurement. In some cases, thesphere value of the vision treatment is determined based on the formulaS=−0.2 C−0.25, where S is the sphere value and C is the pre-operativecylinder value.

High Order Aberrations

Laser-Assisted in situ Keratomileusis (LASIK) treatments, includingconvention and wavefront-guided version, can induce high orderaberrations, and in particular spherical aberration (SA). FIG. 47 showsa scatter plot for a 6M post-operative spherical aberration (SA) as afunction of the pre-operative wavefront refraction in sphericalequivalent (WRSE), with exemplary CustomVue® treatments, for both myopiaand hyperopia. This plot shows a regression slope for hyperopia (e.g.0.0962) that is about three times the slope for myopia (e.g. 0.0364),indicating the difference in the induction strength. Without being boundby any particular theory, it is believed that this difference may be theresult of a low pass filtering process, such as that described inpreviously incorporated U.S. Patent Application No. 61/708,815 filedOct. 2, 2012.

FIG. 48 provides plots for a target SA change (e.g. addition for SA) asa function of pre-operative WRS (wavefront refraction in sphere; upperpanel) and WRC (wavefront refraction in cylinder; lower panel),according to embodiments of the present invention. These plots are basedon a simulation conducted with 327 myopic eyes (e.g. simulated additionfor the deconvolved target as compared to an original target for 327simulated myopic eyes). A multivariate regression was used to obtain thefollowing regression formula: ΔSA=−0.0385S+0.0364C−0.033. This equationindicates that both pre-operative sphere (S) and cylinder (C) have aneffect on the SA addition. To determine a tolerance for theverification, it is possible to consider the 95% confidence interval forall the three parameters in the equation. The 95% confidence intervalfor the sphere slope is [−0.0402, −0.0368], that for the cylinder slopeis [0.0305, 0.0424] and that for the constant term is [−0.0428,−0.0232]. The p-values for each of them are much smaller than 0.001. Theadjusted R-square is 0.857. A range of ±0.15 was determined so the upperand lower bounds can be expressed with the following equations:

ΔSA⁻=−0.0385S+0.0364C−0.183  (Equation 34)

ΔSA₊=−0.0385S+0.0364C+0.117  (Equation 35)

Based on the plots in FIG. 48, it can be seen that post-operative SA canbe related to pre-operative sphere, pre-operative cylinder, or both.Hence, sphere and/or cylinder can contribute to the post-operativeinduction of SA. The upper panel illustrates a stronger correlation forSA (high order aberration) and sphere (wavefront refraction in sphere).The lower panel illustrates a weaker correlation for SA (high orderaberration) and cylinder (wavefront refraction in cylinder). Based on acomparison between FIG. 47 and the upper panel of FIG. 48, it can bedetermined that the deconvolved target provides good compensation,because there is a match between the plots.

According to some embodiments, validation techniques can involvecomparing a revised target with an original target, and determiningwhether the revised target is sufficiently similar to the originaltarget. For example, with regard to FIG. 48, it is possible to observe atrend line with a slope of −0.353 which matches the observed trend lineslope of −0.0364. For a −6 D case, as an example, FIG. 48 shows SA ofabout 0.15 um. According to some embodiments, validation techniques caninvolve calculating the SA associated with a revised target, comparingthat SA with the SA of an original target, and determining whether thedifference between the revised target SA and the original target SAmeets a certain criteria. For example, the difference can be positive,indicating an effective induction of positive SA in the revised targetSA.

FIG. 49 provides a comparison between observed and expected additionsfor the deconvolved target as compared to an original target forpost-operative spherical aberration. When Equations (34) and (35) areused for the 327-eye dataset, the additional SA obtained by doingdeconvolved−[minus] original targets, is within the upper and lowerbounds for all eyes. This can provide an indication of what thedeconvolution is introducing into the target shape. FIG. 49 depicts theresult shown as a function of WRSE. As illustrated here, the additionhas a slope that is similar to the slope of the observed induction ofSA, indicating a removal of this SA induction trend. According to someembodiments, it is possible to use information such as this to validatea design algorithm and/or to verify that a software code is implementedcorrectly (e.g. alleviate the induction of post-operative SA). Forexample, where an original treatment may induce positive SA, a revisedtreatment may counteract that effect by providing a negative SA. In somecases, a revised treatment target can have a greater positive SA for thesame dioptric correction. In some cases, a revised treatment target cancreate an negative SA to counteract an observed clinical SA. In somecases, a kernel can be used to generate a treatment that does not induceexcessive SA.

FIG. 50 depicts aspects of a treatment validation process 5000 accordingto embodiments of the present invention. As shown here, a modifiedtreatment target 5020 can be generated based on an original treatmenttarget 5010, for example by using a modification process 5015. In somecases, a modification process 5015 can include a deconvolution process,a low pass filter process, a scaling process, or an adjustment process,as discussed elsewhere herein, or any combination thereof. An inducedaberration 5030 (e.g. a high order aberration such as sphericalaberration) can be determined for the original target, and an inducedaberration 5040 (e.g. high order aberration such as sphericalaberration) can be determined for the modified target. According to someembodiments, the induced aberrations can correspond to post-operativeinduced HOAs. The induced aberrations can be compared, as indicated bystep 5050. The modified treatment target can be validated based on thecomparison of the induced aberrations, as indicated by step 5060. Forexample, the modified target can be validated if the difference betweeninduced aberration 5030 and induced aberration 5040 meets a certaincriteria or threshold. Relatedly, the modification process 5015 (whichoptionally may include a deconvolution process, a low pass filterprocess, a scaling process, or another adjustment or modificationtechniques as disclosed herein) for obtaining the modified target can bevalidated in a similar fashion, based on the comparison.

According to some embodiments, a filter can be validated based on acomparison between simulated and observed post-operative SE and SA fordifferent data sets. For example, as depicted in the data sets of FIGS.51 and 52, for example, there is a close match between the simulated andobserved data trend lines.

For example, FIG. 51 shows a comparison between simulated and observed(6M) post-operative aberrations for a clinical trial (myopic eyes, n=74)and data (myopic eyes, n=72). As shown here, it is possibly to verifythe model with two clinical data sets for both SE and SA, meaning themodel works very well. Put another way, FIG. 51 illustrates validationof the optimized filter model for two data sets: clinical trial data(left) and commercial data (right). As shown here, the trend lines forobserved and simulated SA and SE are very close. This result confirmsthat the optimized filter, derived from some different data sets,provides a good model for a post-operative SA versus a pre-operative SEtrend.

Some data sets show a constant shift between simulated and observedtrend lines. Such shifts for post-operative SE or SA trends can be aboutthe same for all pre-operative MRSE values, which means they may notdepend on ablation depth. The data may result from aberrations, causedby the creation of the LASIK flap. Depending on the choice ofmicrokeratome and the individual surgeon technique, the flap-inducedaberrations may differ from site to site or surgeon to surgeon.Simulations of the predicted post-operative outcome for modified targetsmay assume no flap-induced aberrations.

According to some embodiments, filter techniques as disclosed herein canprovide a close match of observed vs. predicted post-operative trendsnot only for SE and SA, but also for secondary spherical aberration.FIG. 52 depicts plots corresponding to eye study data (n=390), myopiceye (n=74, n=72) data, and additional eye data (n=76), which providecomparisons of simulated and observed post-operative secondary sphericalaberrations.

Techniques as disclosed herein can also explain at least partially(about one third) of a cylinder coupling effect (e.g. post-operativesphere vs. pre-operative cylinder trend). FIG. 53 depicts a comparisonbetween simulated and observed post-operative (6M) sphere vs.pre-operative cylinder tends for myopia eyes (with WFD=6 mm), where WFDrepresent wavefront diameter.

It can be seen that certain vision conditions, including for examplemyopia, the presence of pre-operative cylinder can affect thepost-operative sphere outcome. In many cases, a greater pre-operativecylinder (in the minus cylinder notation) can correspond to a greatersphere post-operative over-correction (hyperopic shift). By usingcertain data (e.g. clinical data), it is possible to evaluate the finaloutcome and make the appropriate adjustment.

FIG. 53A depicts results from a study involving 334 eyes. A plot of theintended versus achieved is provided for Manifest (upper panel) andiDesign SE (lower panel). As shown here, the slope is relatively closeto unity but there is an offset of about 0.38 D for MRSE and 0.30 D forwavefront refraction in spherical equivalent (WRSE). In addition, aresidual coupling (post-op sphere versus pre-op cylinder) can still beseen, again, with manifest and iDesign refractions. The residual slopeis about −0.067, as depicted in FIG. 53B.

To remove the residual cylinder coupling slope and intercept, thefollowing algorithm is proposed, MRS target adjustment=−0.38−0.28*idc0,where idc0 stands for pre-operative iDesign cylinder at zero vertex.With this algorithm, the expected outcome as compared to the actualoutcome (intended vs achieved) can be shown as depicted in FIG. 53C(upper panel). As shown here, the new slope is closer to unity and theintercept is zero or close to zero. With this algorithm, the expectedpost-op mean MRSE can be −0.05 D, and post-op mean MRS can be +0.12 D.The distribution of the refractive outcome can be shown in FIG. 53C(lower panel).

Accordingly, an exemplary method of determining a vision treatment foran eye of a patient can include receiving or obtaining a pre-operativecylinder value for the eye of the patient, and determining the visiontreatment for the eye, where the vision treatment includes a spherevalue that is based on the pre-operative cylinder value. The spherevalue of the vision treatment can be determined based on the formulaS=−0.28C−0.38, where S is the sphere value and C is the pre-operativecylinder value.

Additional Aspects Related to Reduction of Post-Surgical SphericalAberration

Embodiments of the present invention encompass systems and methods forreducing or eliminating spherical aberration that may be induced bysurgical treatments for myopia. Often, such approaches can be based ontechniques that involve scaling a treatment algorithm such that with anSA reduction algorithm, it is possible to obtain a slope of unity in theintended vs achieved MRSE plot. Clinical data has been obtained whichconfirms such slopes are at unity or substantially at unity. FIGS.53A-58 encompass data obtained from an iDesign™ US IDE clinical trial(e.g. which may not include an SA reduction algorithm). Embodiments ofthe present invention encompass the implementation of algorithms toremove or reduce a cylinder coupling effect. As discussed elsewhereherein, a coupling effect algorithm can be based on the relationshipS=−0.28 C−0.38 for a sphere adjustment in a pre-operative refraction.Such approaches can achieve a near unity slope in the intended vsachieved MRSE plot. At the same time, it is observed that cylindercoupling is reduced or eliminated. The contents of FIGS. 53A-58 supportscaling approaches such as those depicted in FIGS. 41 and 42.

As discussed elsewhere herein, diagnostic systems such as WaveScan® andiDesign™ devices can be used to evaluate spherical aberration in an eyeof a patient. For example, such diagnostic devices can assess targetinduced spherical aberration in a post-operative patient. Sphericalaberration can correspond to a fourth order rotationally symmetricZernike term in the description of wavefront aberrations of an eye. Anexemplary iDesign™ diagnostic device can incorporate multiplemeasurements, including wavefront aberrometry measurements, cornealtopography measurements, autorefractometry measurements, keratometrymeasurements, and pupillometry measurements.

As shown in FIG. 54, a statistically significant trend in myopictreatments can be observed for the induction of (primary) sphericalaberration following a laser vision correction procedure such as certainCustomVue® Laser-Assisted in situ Keratomileusis (LASIK) treatments.FIG. 54 (upper panel) depicts results at 6 months post-operative using aWaveScan® technique, and FIG. 54 (lower panel) depicts results at 6months post-operative using an iDesign™ technique. As shown here, theslope for myopia can be similar, with a −0.031× value in the upper panel(WaveScan®), and a −0.0339× value in the lower panel (iDesign™)

Various mechanisms may be implicated in the induction of sphericalaberration in laser vision correction, including for example (i) theinduction of primary SA due to a target shape as discussed elsewhereherein, (ii) biomechanical changes such as peripheral stromal thickeningor peripheral effects associated with flap cutting, (iii) peripheralunder-ablation for example which may be associated with peripheral laserenergy loss that is not property accounted for, and (iv) epithelialremodeling. According to some embodiments, reducing or eliminating theinduction of post-operative SA may involve increasing the amount ofablation performed in the periphery of the target shape.

FIG. 55 depicts aspects of differential shapes relative to a referenceablation profile, for ablation depth difference (upper panel) andablation curvature difference (lower panel). As shown here, differentshape options (de-convolved, dOZ, dK, and SA shift) can have differenteffects (e.g. impact on ablation depth or ablation curve) in the contextof surgical procedures for reducing spherical aberration.

The dOZ line corresponds to an increase or extension in optical zone. Asdiscussed elsewhere herein, a target shape or ablation target profilecan include an optical zone and a transition zone. The aggregate of theoptical zone and transition zone may be referred to as an ablation zone,corresponding to the entire corneal region covered by a laser ablation.The optical zone may refer to a corneal region which received a fullintended refractive treatment. A transition zone may refer to a cornealregion outside of the optical zone but inside of the ablation zone.

As an illustration, to obtain a 6 mm optical zone that has minimal or nospherical aberration, it may be desirable to extend or increase theoptical zone by 0.85 mm (e.g. to 6.85 mm) and ablate a larger zone (e.g.8.85 mm). As such, there may be a transition zone peripheral to theoptical zone (e.g. transition zone of 2 mm). Exemplary OZ×AZ parameterscan include based values of 6 mm×8 mm for myopia and 6 mm×9 mm forhyperopia and mixed astigmatism. As depicted here, however, increasingthe optical zone can increase the ablation depth (e.g. to about 40 μm ormore for an 8D ablation) to a greater extent than the other techniques.Because in some cases it may be desirable to select treatments havinglower ablation depths rather than higher ablation depths, it may bepreferable to use other options as an alternative to increasing orextending the optical zone. For example, the deconvolution lineindicates that a deconvolution approach has a minimal impact on ablationdepth (e.g. less than 10 μm) and is consistent with an expectedphysiological response.

Similarly, the SA shift (e.g. increase SA by 0.378 μm for −8 Diopters)line indicates that an approach involving (primary) SA shift also has aminimal impact on ablation depth (e.g. less than 10 μm). Put anotherway, it is possible to add 0.378 μm to an initial SA value to obtain anew SA value, where the initial SA value corresponds to pre-operativeSA.

As shown in the upper panel of FIG. 55, the dK line (e.g. increase inkeratometry value, for example 25 Diopters) indicates that an approachinvolving an increase in keratometry values can provide an intermediateincrease in ablation depth, such that the ablation depth change is lowerthan the dOZ line and greater than the deconvolution and SA shift lines.In other words, it is possible to add 25 Diopters to an initialkeratometry Diopter value to obtain a new keratometry Diopter value, andthe initial value can be obtained by a keratometer or by an iDesign™device.

The lower panel of FIG. 55 indicates that an approach involving anincrease or extension in optical zone (dOZ line) can involve an ablationshape curvature change profile that is more extreme than the ablationshape curvature change profiles observed with other techniques(deconvolution, increase in keratometry, SA shift).

In some cases, it is possible to combine the use of a deconvolutionkernel (as discussed elsewhere herein) with a shape option techniquecorresponding to the SA shift depicted in FIG. 55. The SA shift can bebased on a correlation between postoperative spherical equivalent andpreoperative spherical equivalent. For example, a decreasedpostoperative spherical aberration can correspond to an increasedpreoperative spherical aberration.

In some cases, it is possible to combine the use of a deconvolutionkernel with a shape option technique corresponding to the increased orshifted keratometry value depicted in FIG. 55. As depicted here, forexample, the increased keratometry value can correspond to an increaseof 25 D to every eye.

In some cases, it is possible to combine the use of a deconvolutionkernel with a shape option technique corresponding to the SA shift aswell as a shape option technique corresponding to the increased orshifted keratometry values.

FIG. 55 depicts ablation depth and curvature changes for the treatmentsin isolation (e.g. a pure deconvolution approach, a pure optical zoneextension approach, a pure keratometry increase approach, and a purespherical aberration shift approach). As shown here, an optical zoneincrease/extension approach can be the most costly in terms of tissuedepth.

According to some embodiments, when combining approaches, it may bepossible to selectively weight or adjust the impact provided by theindividual approaches. For example, it is possible to use a 25D increasein keratometry value (as depicted in FIG. 55) in combination with apercentage of the 0.378 um SA shift (also depicted in FIG. 55). For bothkeratometry and pre-op SA, the simulation can use the addition ofkeratometry value as a multiple of the pre-operative SE, for example,0.5×, 1.0×, 2.0×, and the like. Hence, for example, where keratometryvalue increases by 25 D, there may be an increase, such as a percentageof preoperative SE, e.g. 0.5×, 1.0×, 2.0×, and the like. Similarly, itis possible to use a multiple for the pre-operative SA values, such as1.2×, 1.5×, 2.0×, and the like (e.g. larger than the measured value).

Hence, FIG. 55 depicts a comparison of outcomes corresponding to variousapproaches of reducing SA, as discussed elsewhere herein.

An exemplary deconvolution approach can involve applying a filter (suchas a low pass filter or optimized linear filter) to an originaltreatment target profile so as to obtain a deconvolved target profile.As discussed elsewhere herein, it is possible to generate a visiontreatment based on a deconvolved target profile. According to someembodiments, a filter (deconvolution) approach is based on a biologicalmechanism (e.g. related to healing). In some cases, a filter approachcan be implemented to address any of a wide variety of indications,including multi-focal corrections. Filter approaches are found toprovide a good fit to observed data (e.g. from clinical studies).According to some embodiments, an increase in ablation depth associatedwith the deconvolution approach may correspond to a preservation ofcentral curvature in the deconvolved target profile. Exemplary aspectsof ablation depth are depicted in FIG. 56 (lower panel).

As shown in the upper panel of FIG. 56, (which corresponds to 6 monthpostoperative data) the observed relationship between postoperativespherical aberration (SA) and preoperative manifest refraction sphericalequivalent (MRSE) has a slope of about −0.0353. The simulatedrelationship between postoperative SA and preoperative MRSE has a slopeof about −0.0445. The simulated outcome can be obtained using a kernelwith three parameters and two correlations. The expected values can beobtained by using the same kernel that is used to obtain the simulatedvalues. The expected relationship between postoperative SA andpreoperative MRSE has a slope of about −0.0103, which is lower than theslope for the observed data and also lower than the slope for thesimulated data. As shown here, the observed and simulated slope valuesare similar, and the observed data values present a higher spread.

As illustrated in the lower panel of FIG. 56, the extra ablation depthdue associated with a deconvolution approach can correspond to thepreoperative MRSE. For example, a more negative preoperative MRSE cancorrespond to a higher extra ablation depth, and a less negativepreoperative MRSE can correspond to a lower extra ablation depth. Insome cases, a relatively small extra ablation depth can correspond toimproved or enhanced safety.

In an exemplary clinical study, the right and left eyes of each patientpresent similar or substantially similar refraction properties. For anindividual patient, one eye is treated using a test deconvolutionalgorithm and the other eye is treated using a reference deconvolutionalgorithm. In some cases, the test eye can be treated usingimplementation of an SA reduction algorithm, on top of a CustomVue™algorithm. The control (or reference) eye can be treated using aCustomVue™ algorithm only. Data from an SA reduction study (e.g.implementing the deconvolution algorithm on top of a CustomVue™algorithm) can be different from iDesign™ data from a US IDE clinicaltrial (which implements a CustomVue™ algorithm). A paired eye randomizedcomparison can be performed to evaluate the test and referenceapproaches. The patients of the clinical study present with a variety ofmyopia conditions. In some cases, patients have myopia with MRSE withina range from −4D to −12D. In some cases, patients have high astigmatism.Patients can be evaluated before treatment, and also followingtreatment, for example at one day postoperation, one week postoperation,one month postoperation, and three months postoperation. Treatmentparameters can involve, for example, a 6 mm optical zone and an 8 mmablation zone.

Study variables can include high order aberrations such as sphericalaberration (Z4) from wavefront measurements (e.g. Zernike technique),uncorrected visual acuity (UCVA), best corrected visual acuity (BCVA),refraction (manifest and wavefront), optical coherence tomography (OCT),and subjective questionnaires. In some cases, some patients present withmyopia with spherical equivalent measurements within a range from 4D to6D, some patients present with myopia with spherical equivalentmeasurements within a range from 6D to 8D, and some patients presentwith myopia with spherical equivalent measurements within a range from8D to 10D. Less common are patients presenting with myopia withspherical equivalent measurements within a range from 10D to 12D. The Dvalues discussed in the paragraph are absolute values (e.g. positivenomenclature) corresponding to negative D values such as those depictedin FIG. 56. Hence, where this paragraph mentions a range of 10D to 12D,the values are −10 D to −12 D.

FIG. 57 provides an analysis of postoperative diagnostic (e.g.wavefront) measurements, for example high order aberrations. The meanand standard deviation (standard error) are depicted. The error bars are1.96× the standard error (e.g. corresponding to 95% confidence levels).The high order aberration evaluated in the upper panel include a 4^(th)order Zernike, and specifically the primary spherical aberration (Z₄ ⁰).The high order aberrations evaluated in the lower panel include 3^(rd)order to 6^(th) radial order Zernikes (e.g. Z₃ to Z₆), which for examplecan include the 6^(th) to 27^(th) terms, such as secondary sphericalaberration (Z₆ ⁰). Zernike modes of the third order and higher can beconsidered as high order aberrations, whereas Zernike modes of thezeroth through second order can be considered as low order aberrations.

When evaluating the control and study eyes in the upper panel of FIG.57, it can be seen that the primary spherical aberration (Z₄ ⁰) is muchlower in the study eyes as compared to the control eyes.

A comparison of the upper and lower panes of FIG. 57 reveals that thedifference in postoperative high order aberrations between the referencecontrol eyes and the test study eyes is significantly impacted by theprimary spherical aberration. Hence, the other high order aberrationscan have less of an impact on or contribution to the overall high orderaberrations. In this way, it can be seen that postoperative primaryspherical aberration can be a primary contributor to the overallpostoperative aberrations, and that the test study treatment approachcan produce a significantly lower amount of postoperative sphericalaberration as compared to the reference control treatment approach. Itis also observed (but not shown in FIG. 57) that MRSE outcomes for testand control eyes were similar at three months postoperation.

When performing a vision treatment, it is possible to create a cornealflap using, for example, a femtosecond laser or a mechanicalmicrokeratome. The results in the upper and lower panels are obtainedusing a femtosecond laser. As shown here, there is an increase inprimary spherical aberration when comparing the one week and one monthresults, and a stabilization of primary spherical aberration whencomparing the one month and three month results.

As discussed elsewhere herein, it is possible to implement a kernelbased on a correlation between postoperative defocus and preoperativedefocus (e.g. postoperative defocus as a function of preoperativedefocus). Similarly, it is possible to implement a kernel based on acorrelation between postoperative spherical aberration and preoperativemanifest refraction spherical equivalent. In some cases, it is possibleto generate a kernel based on either or both of these correlations.

In some cases, it is possible to generate a kernel based on additionalcorrelations. For example, a kernel can be based on a correlationbetween postoperative spherical aberration and preoperative sphericalaberration. Similarly, a kernel can be based on a correlation betweenpostoperative secondary spherical aberration and preoperative manifestrefraction spherical equivalent.

Defocus (also known as spherical equivalent) refers to the center modeof the three Zernike second radial order aberration modes. Specifically,defocus refers to the Z₂ ⁰ aberration, and corresponds with the averagesphere power of the wavefront. The remaining two second order modes, Z₂⁻² and Z₂ ², correspond to the cylinder power. Collectively, the threesecond radial order aberrations can characterize the curvature orvergence of a wavefront.

FIG. 58 schematically illustrates techniques for obtaining andimplementing a modified target shape, according to embodiments of thepresent invention. As shown here, study data can be used to deriveparameters of a kernel for simulating a low-pass filtering process, forcorneal healing and the like. Embodiments may also include optimizingthe parameters by using a clinical data set. These techniques may alsoinvolve evaluating the extent to which observed spherical aberration isattributed to error, due to an imperfect optical treatment shape. Insome instances, methods may also include addressing target shape inducedSA by providing transition zone adjustments, optical zone extensionadjustments, or both. In some cases, a deconvolution (e.g. inverse oflow pass filter) may boost the total treatment depth. Techniques mayalso involve running a revised target controller (e.g. without a cosineeffect) with a low-pass filter, to evaluate the extent to which SA for aclinical data set correlates with observed SA, or to evaluate the extentto which post-operative refractions correlate with what is expectedbased on the clinical data. The Optimized Kernel Parameter can berelated to LPF, and sigma can represent the diffusion coefficient.Hence, as shown in FIG. 58, with a clinical data set 5810, a kerneloptimization process 5812 can be employed such that simulation can beperformed to obtain the optimized kernel parameter (sigma) 5814.

As discussed elsewhere herein, exemplary systems and methods canimplement dual scale kernel techniques, triple scale kernel techniques,and other multi-scale kernel techniques (e.g. multiple parameters in ahealing kernel). According to some embodiment, the value ofsigma=[0.0229, −0.305, 0.919] was found to correspond to an optimizedkernel parameter. Specifically, a three parameter case where the generaloptimized linear filter (OLF) formula is given by:

${K\left( {{xi},{yi}} \right)} = {\frac{1}{1 + \left( {{r/s}\; 2} \right)^{2} + \left( {{r/s}\; 4} \right)^{4} + \left( {{r/s}\; 6} \right)^{6}}.}$

Here, s2, s4, and s6 are the three parameters, where s2=0.0229,s4=−0.305, and s6=0.919.

For a practical implementation, the clinical data 5810 can be sent to aresearch version of Target Controller 5818 (in matlab), which isidentical to the production Target Controller 5826 (in C++). It can bederived from the Target Controller 5818 that induction of sphericalaberration (SA) 5820 occurs in the target so a removal of atarget-induced SA can be implemented in a revised Target Controller5822. The revised Target Controller 5822 can implement a new opticalzone (OZ) extension algorithm 5828, and a new Transition Zone algorithm5830. With all the revisions, the Revised Target Controller 5822 can betested with data set 5824, which can be the same as (or different from)data set 5810. The Revised Target Controller 5822 can then be verifiedwith SA and MRSE (manifest refraction in spherical equivalent) in 5832.

According to some embodiments, an optimized kernel parameter and/orscaling factor can be modified or obtained based on techniques involvingan increase in keratometry and/or an increase in spherical aberration.For example, as depicted in FIG. 58, a kernel optimization process 5812can take into account an increase in keratometry 5811 and/or an increasein SA 5813, such that simulation can be performed to obtain theoptimized kernel parameter (sigma) 5814. As shown here, values fors=[0.0229−0.305 0.919] and f=0.7489 can be implemented in a productioncode, for example for use in clinical trials and other treatments.

All patent filings (including patents, patent applications, and patentpublications), scientific journals, books, treatises, technicalreferences, and other publications and materials discussed in thisapplication are incorporated herein by reference in their entirety forall purposes.

A variety of modifications are possible within the scope of the presentinvention. A variety of parameters, variables, factors, and the like canbe incorporated into the exemplary method steps or system modules. Whilethe specific embodiments have been described in some detail, by way ofexample and for clarity of understanding, a variety of adaptations,changes, and modifications will be obvious to those of skill in the art.Although the invention has been described with specific reference to awavefront system using lenslets, other suitable wavefront systems thatmeasure angles of light passing through the eye may be employed. Forexample, systems using the principles of ray tracing aberrometry,tscherning aberrometry, and dynamic skiascopy may be used with thecurrent invention. The above systems are available from TRACEYTechnologies of Bellaire, Tex., Wavelight of Erlangen, Germany, andNidek, Inc. of Fremont, Calif., respectively. The invention may also bepracticed with a spatially resolved refractometer as described in U.S.Pat. Nos. 6,099,125; 6,000,800; and 5,258,791, the full disclosures ofwhich are incorporated herein by reference. Treatments that may benefitfrom the invention include intraocular lenses, contact lenses,spectacles and other surgical methods in addition to refractive lasercorneal surgery.

Each of the calculations or operations discussed herein may be performedusing a computer or other processor having hardware, software, and/orfirmware. The various method steps may be performed by modules, and themodules may comprise any of a wide variety of digital and/or analog dataprocessing hardware and/or software arranged to perform the method stepsdescribed herein. The modules optionally comprising data processinghardware adapted to perform one or more of these steps by havingappropriate machine programming code associated therewith, the modulesfor two or more steps (or portions of two or more steps) beingintegrated into a single processor board or separated into differentprocessor boards in any of a wide variety of integrated and/ordistributed processing architectures. These methods and systems willoften employ a tangible media embodying machine-readable code withinstructions for performing the method steps described above. Suitabletangible media may comprise a memory (including a volatile memory and/ora non-volatile memory), a storage media (such as a magnetic recording ona floppy disk, a hard disk, a tape, or the like; on an optical memorysuch as a CD, a CD-R/W, a CD-ROM, a DVD, or the like; or any otherdigital or analog storage media), or the like. While the exemplaryembodiments have been described in some detail, by way of example andfor clarity of understanding, those of skill in the art will recognizethat a variety of modification, adaptations, and changes may beemployed.

The methods and apparatuses of the present invention may be provided inone or more kits for such use. The kits may comprise a system fordetermining a treatment for an eye of a patient, and instructions foruse. Optionally, such kits may further include any of the other systemcomponents described in relation to the present invention and any othermaterials or items relevant to the present invention. The instructionsfor use can set forth any of the methods as described herein.

While the above provides a full and complete disclosure of exemplaryembodiments of the present invention, various modifications, alternateconstructions and equivalents may be employed as desired. Consequently,although the embodiments have been described in some detail, by way ofexample and for clarity of understanding, a variety of modifications,changes, and adaptations will be obvious to those of skill in the art.Accordingly, the above description and illustrations should not beconstrued as limiting the invention, which can be defined by the claims.

1. A method of determining a vision treatment for an eye of a patient,the method comprising: receiving, at an input, an original targetprofile for the eye of the patient; obtaining a deconvolved targetprofile based on the original target profile and a low pass filter;obtaining a scale factor, wherein the scale factor is based on a loworder refraction measure of a test eye population and a low orderrefraction measure of a convolved test eye population profile, andwherein the convolved test eye population profile is based on aconvolution of the test eye population profile; determining a scaledtarget profile based on the deconvolved target profile and the scalefactor; and determining the vision treatment based on the scaled targetprofile.
 2. The method according to claim 1, wherein the low pass filteris an optimized linear filter.
 3. The method according to claim 1,wherein the scale factor has a value within a range from about 0.4 toabout 0.8.
 4. The method according to claim 1, wherein the scale factorhas a value of about 0.7489.
 5. The method according to claim 1, whereinthe low order refraction measure of the test eye population profilecomprises a first manifest refraction spherical equivalent measure andthe low order refraction measure of the convolved test eye populationprofile comprises a second manifest refraction spherical equivalentmeasure.
 6. The method according to claim 5, wherein the first manifestrefraction spherical equivalent measure is a 4 mm refraction measure andthe second manifest refraction spherical equivalent measure is a 4 mmrefraction measure.
 7. A method of determining a vision treatment for aneye of a patient, the method comprising: receiving, at an input, anoriginal target profile for the eye of the patient; determining a firstlow order refraction measure based on the original target profile;obtaining a deconvolved target profile based on the original targetprofile and a low pass filter; determining a second low order refractionmeasure based on the deconvolved target profile; determining a scalefactor based on a comparison between the first and second low orderrefraction measures; determining a scaled target profile based on thedeconvolved target profile and the scale factor; and determining thevision treatment based on the scaled target profile.
 8. The methodaccording to claim 7, wherein the first low order refraction measurecomprises a first manifest refraction spherical equivalent measure andthe second low order refraction measure comprises a second manifestrefraction spherical equivalent measure.
 9. The method according toclaim 8, wherein the first manifest refraction spherical equivalentmeasure is a 4 mm refraction measure and the second manifest refractionspherical equivalent measure is a 4 mm refraction measure.
 10. Themethod according to claim 7, wherein the first low order refractionmeasure comprises a first sphere measure and the second low orderrefraction measure comprises a second sphere measure.
 11. The methodaccording to claim 7, wherein the first low order refraction measurecomprises a first cylinder measure and the second low order refractionmeasure comprises a second cylinder measure.
 12. A method of determininga vision treatment for an eye of a patient, the method comprising:receiving, at an input, an original target profile for the eye of thepatient; obtaining a first healed profile based on the original targetprofile; obtaining a deconvolved target profile based on the originaltarget profile and a low pass filter; obtaining a second healed profilebased on the deconvolved target profile; determining a first low orderrefraction measure based on the first healed profile; determining asecond low order refraction measure based on the second healed profile;determining a scale factor based on a comparison between the first andsecond low order refraction measures; determining a scaled targetprofile based on the deconvolved target profile and the scale factor;and determining the vision treatment based on the scaled target profile.13. The method according to claim 12, wherein the first low orderrefraction measure comprises a first manifest refraction sphericalequivalent measure and the second low order refraction measure comprisesa second manifest refraction spherical equivalent measure.
 14. Themethod according to claim 13, wherein the first manifest refractionspherical equivalent measure is a 4 mm refraction measure and the secondmanifest refraction spherical equivalent measure is a 4 mm refractionmeasure.
 15. The method according to claim 12, wherein the first loworder refraction measure comprises a first sphere measure and the secondlow order refraction measure comprises a second sphere measure.
 16. Themethod according to claim 12, wherein the first low order refractionmeasure comprises a first cylinder measure and the second low orderrefraction measure comprises a second cylinder measure.
 17. A method ofdetermining a vision treatment for an eye of a patient, the methodcomprising: receiving, at an input, an original target profile for theeye of the patient; obtaining a deconvolved target profile based on theoriginal target profile and a low pass filter; obtaining a scale factor,wherein the scale factor is based on a low order refraction measure of atest eye population and a low order refraction measure of a convolvedtest eye population profile, and wherein the convolved test eyepopulation profile is based on a convolution of the test eye populationprofile; determining a scaled target profile based on the deconvolvedtarget profile and the scale factor; adjusting a sphere parameter of thescaled target profile based on a pre-operative cylinder measurement ofthe eye of the patient; and determining the vision treatment based onthe adjusted target profile. 18.-23. (canceled)